Saying something is better for EH when it is the only one for EH is a bit of a no-brainer--but that does not, by default, make it a better trinket. I think that is an example of taking the 'EH > everything, regardless of quantity' a bit too far.
The comparison to mana regen for healers is not the same, as mana regen is something that specifically becomes of zero use once a certain gear threshold is met. 172 Dodge Rating never becomes of zero use to a tank, nor does the armor proc.
Although EH certainly has major benefits, Dodge will contribute to you avoiding death in many cases. When the quantity of the values is so disparate, it's certainly worth considering dropping the 'EH > everything, regardless of quantity' mentality, IMO. Comparing 20 Dodge Rating gems to 30 Stamina gems is totally different to comparing 172 Dodge Rating to 111 Stamina. That is even before the armor proc, which has pretty high uptime and is not particularly 'unreliable' (if you are in a situation where 111 Stamina would help you considerably, you are in a situation where you will drop below 35% and trigger the trinket, it is not random.)
Unless the fight is purely magical, you are probably making a choice that is detrimental to your long-term chance of survival to take such a statistical hit just for a bit of extra Stamina.
If you said Flawless Fang, Skeleton Key, Glyph of Indom, Balebrew Charm, Satrina's Scarab, The Black Heart (considering the armor proc), or even the Heart of Iron I would most likely agree in all those cases... but Essence of Gossamer seems a bit over the top.