Blizz is playing within a state of dynamic balance that occasionally veers off a bit for a particular encounter because they didn't expect some combination of interplaying elements. The game isn't always imbalanced for that sense, so much as Blizz is constantly trying to keep an even keel with their changes. So tricky language here.
Balance in a simple system, such as the physical item a balance, you have two elements that you are keeping a desired keel between (maybe 50/50 even, maybe 70/30 for one element, etc). In a complex system such as WoW there is no such simple balancing point. Balance instead is a complex act of plate spinning. As tanks we have an assortment of elements that need to be balanced and while we can try to reduce them for simplicity of consideration they actually are not readily simplifiable, nor do they lend themselves to a A vs B balance.
One of the simplest examples would be the interplay of Mitigation (compound of armor, stance, resistance and considered in both passive and burst via CDs), Avoidance (easy to lump all the elements together though they come from many internal and external sources), and Health as played against damage the tank takes with the elements of hit size, hit frequency/speed, and special abilities or increased periods of damage. We've seen this play out with elements such as Chill of the Thrown.
If Avoidance is too high for fixed Armor and Health, then to keep a consistent level of damage taken by the tank the hits have to be very large (leading to boom/bust tank health and spammed healing required to not lose the tank to an couple hits without heals in the middle). There are a great many elements that contribute, and toying with any one of them will require adjustments in every other, not just an A vs B trade off. This is the intrigue of playing the game as well, as a simple A vs B balance is easy to read and boring, it leaves little room for the player.
Ideally each tank will be coming from its unique class and semi-unique tree. I think they did an admirable job in making the three DK trees feel as different as they do for the common root elements and tools. The post-BC drive is that each tank should not be incapable (as the true inverse of viable, which is a horribly misused buzzword in the WoW community) of completing any encounter because of their class/spec mechanics.
We all get there by a different means but that doesn't mean that we can't or shouldn't be equally capable of addressing the challenge in our own fashion. At the same time, no class/spec mechanic should offer a benefit so significant that it trivializes other elements in the equation. For example, the tank should not have a cooldown that matches an important encounter element so significantly that you can bring a noticeably under-geared tank of that class/spec and have an easier time of it than a much better geared tank of another class/spec. This is always flavored by the very hard to quantify player element, where a very skilled player may figure out hot to use their tools in such a fashion where many others don't.
I am fairly certain that encounters are not designed to meet the tanks, but rather the encounters are designed to meet a raid team and they then check it against the considerations of all 10 classes/30 specs as needed. Maybe a semantic difference, but you get my distinction?
The flavor is that everyone can apply it, but with varying concerns on how and how many. In order to keep that balanced the encounters simply only need to require that the debuff not be 100% crucial as a make-or-break detail. For example, if you would need to debuff 3 targets at once or the tank will die 80% of the time (random %, 30% or even less would probably suffice), then the Paladin's version of the tool would be insufficient as a tanking toolbox item, and you would be legitimately able to say, "a Paladin tank is not viable in this situation."
As I said above, RE: #2, I don't believe encounters are balanced to meet the tanks, but rather tanks tools are balanced such that it shouldn't be a concern to change encounters to face any possible combination of raid team compositions.
This is something of a side point, but Disarm is only available from one tank, but from a few classes. There are disarmable mobs and bosses in current progression content, but it is true, I would agree that they don't want it to be an essential ability for make-or-breaking the encounter since it is hard to rely on its availability. Generally, this is an ability that has been reserved for greatest significance in PvP.
This is an example of the differentiation in the tools. Each has its merits and its disadvantages. Vindication is single-target only, requires a sometimes out of the way talent to get for Prot Paladins, and has a limit restricted by the availability of Judgment for use. But as you said, Protadins are judging constantly anyway so its an added benefit to what they do rather than a new thing they have to add to the rotation.
Demo Shout on the other hand is an AoE ability that will apply it everywhere in a close range (which can be improved by talents for range and in scale to match Vinidication's size of reduction). It does require a GCD though, and may not be an attractive item to use if the debuff isn't otherwise required.
But, as an example this is a big pointer at another important detail: What do you identify as a tanking toolbox item, and what is a raid buff?
There are 3 easy tanking debuffs that contribute to the survival of the tank in a meaningful way: melee de-haste, AP reduction, and miss chance. The first can be applied by all tanks (with the distinctions above, every tank can maintain it on a boss easily, but some cannot apply it to a large group, or at least not easily/reliably), to that end you could assume that Blizzard considers it an obligatory anti-boss tool, but a privilege against large groups. This debuff can also be delivered in the full or reduced form by some DPS specs removing the tank's obligation. The AP reduction can be offered by multiple sources, but it can only be applied by 3 of the 4 tanks (poor DKs got the short-end). That said, again, the Paladin can only apply it to one target. You could say one of two things then: it is an obligatory tool on bosses and the tank should be able to provide it themselves (then DKs need a fix), but not on large groups. Or, that this is a perk provided by your raid. It is secondary whether it is provided by your tank or by someone else (in which case DKs are not in need of a fix). Just to contrast, now consider the 3% miss chance debuff. There are 4 class/specs that can deliver it and 1 pays a particularly higher price to do so (MM hunters pay the worst price, Boomkin and BM/Surv Hunters could still trade dps to maintain it). This debuff cannot be delivered by a tank, but it impacts our survival in an important fashion.
The fine print here, I think, is that with tools that are available to more than just the tank we have to remember that these elements are not encounters being balanced against each tank, but rather against the range of what raids can bring, and what is reasonable to expect them to have access to. It is reasonable to expect that a raid could have a Hunter or Balance Druid, but it is a calculated issue of whether or not you are applying the 3% miss. Similarly, the other two debuffs can likely be applied by multiple people in your raid, so it is on your team to figure out how you are doing, if at all. As I said, the melee de-haste is available to every tank at least on single targets so it is easy to say Blizzard assumes you have it covered all the time, but how is a matter for your raid team. If you have a dps DK who can provide it, then your Prot Warrior doesn't have to Tclap on a boss, for example. It is all a careful trade.
Alternatively there are the tools that are central and essential to our job as tanks: threat and survival. Threat is one issue that is usually contested over single target vs AoE tools. The critical threshold is never who does it best, but that every tank *can* do it. That is the measure of "viable." Some would say Prot Warriors or Blood DKs are poor at AoE threat compared to a Paladin, Druid, or Frost DK, but that does not make them no longer "viable" it just makes them less appealing for those situations. It is not Blizzard's prerogative to make every tank equal in terms of AoE threat, they only need to be better than the DPS so that it is not an issue if you don't have a favorable alternative.
Alternately there is the concern of single-target threat. Here the concern is the same: a tank only has to be able to out-tps the damage dealers. However, having them able to go toe to toe with each other allows fights like Deathwhisper's hard-mode. There is a concern that tanks are able to perform to a similar standard, if only to keep all the class/specs attractive, but simply because one spec is lower than another in an absolute scale does not mean it is not "viable."
So in terms of threat, provided every tank can reasonably out-threat their damage dealers, it is not a crucial detail (in general, specific situations it may be) that they can be out-threated by another tank. And at that we get a skewed and personal sense of threat. Stats, specs, and the effort of the player make a big difference. It is not usually fair to say, "I cannot out-threat X when I'm playing Y, so Y or X must be broken or unfair, please fix it." Generally speaking the regulation will be done at an objective level by Blizzard but it is something of an Archimedean point, as you are never free of the variables of player skill.
Automation is not a nice solution because it takes the player out. The thing that makes the game hard to maintain in balance (i.e. the Player/Human factor) is also what makes it fun to play. If you take the player out of it, even in part, you are stripping away the fun, bit by bit.
Trying to fix one variable in the equation can also cause its own balance issues.
The last thing here is that is "max player skill" the smart place to balance performance to? Some class/specs may be harder to get peak performance from. To use completely arbitrary examples, if 90% of Paladins reached 90% of the class's potential or better, but only 30% of Warriors reached 90% of the class's potential, should the 100% mark for the two classes be the same? That is another of the factors that is easy to miss, and hard to gauge, making it that much trickier to find the right balance point for developers.
It is exactly my previous point why this isn't really reasonable. If you balance the highest potential of every tank class/spec against every encounter (assuming that is possible which it isn't really) but many more (to use the same arbitrary example) Paladins could play at a higher level than Warriors, then the Paladin would be considered the only "viable" class by players (who abuse the term), and you'd see the forums full of dismissals for the poor fools who want to Warrior tank that encounter.
Here, for the many reasons I mentioned above, I disagree.
Reducing the elements that make tanks "just different" does not make the game better, it strips the things that are fun out of it. Without room for the fully-human experience, or the closest you can approximate that in a computer-scripted game, it is easy to lose the draw and you might as well go play Roulette.