I've given it some thought, and I disagree with your counter-argument.
Given completely random situations, taking the times you need to move into account, 1/6 of those times will be eating into ToeP activation time. The remaining 5/6th of the time you need to move, you are waiting for your ToeP to cool down. These situations allow your ToeP to get "free" recharge time, and should balance the situations where you are forced to move during activation.

In other words: For every situation you can remember where you were forced to move early and waste activation time, there were likely five (all average caveats apply) situations where you had to move and gained free cooldown time on your ToeP.
(Obviously it's a little silly to think the game is out to get you, and forces you to move only when you have the ToeP active)

With this in mind, I think my argument that you get more activations than averages will show, stands. I.e. You get 1 full activation for a 45 second encounter (not the 1/2 that averages imply) and you get 2 activations during a 100 second encounter (not 1.11).

You are correct to some extend. The point, however, still stands that with an activated trinket you are more susceptible to random chance. That is, one time you get the full bonus, the next time you get nothing. Even if in the long run you come out ahead, that unpredictability is undesirable, because barely beating a boss twice is better than wiping horribly one time and totally destroying it the next.

Further, the problem I have noticed is that you cannot always activate the trinket when it is up. It might be too early for that extra DPS, or you are on the move. Thus, I found that the effective cooldown is usually longer than the listed one. This counteracts the effect that you are describing which amounts to "you get the first cooldown for free in a boss fight". Which effect comes out ahead? That depends on the situation and the boss.

That is probably the reason but I disagree with the logic behind it. They put feral AP on some weapons and treated it like a free stat because you never use feral AP and for example spell power at the same time. Yes you can heal and DPS at the same time with ZHC, but how often do you do that, especially in PvE?

How about Mind Quickening Gem. I use that all the time but feel it wasted due to its just me wasting mana faster and only 1 or 2 uses during a fight. Im trying to find the most damage effecient item over a long period of time.

The the MQG equivalent column. It tells you at what level of damage MQG becomes superior to the other trinkets.

Oh, don't get me wrong, I certainly find ToEP to be the superior choice in the vast majority of situations (hence having it equipped on those fights). I'm just saying that for those two items (or Eye of the Beast at a certain gear level) you have to weigh the strengths and weaknesses of each item with consideration to the fight. Early Battleguard attempts come to mind (before your group is able to control the fight with ease) as a situation in which one might give the blue some serious thought.

ToEP is probably one of the worst trinkets to use at patchwerk :) as reed+tear+mqg+rotd are all superior in that fight

The only nobrainer trinket there is for all fights is tear the rest all have their fights where they outshine the rest.

ToEP, best allround trinket with alittle punch. especially nice for trash where it cooldowns between pulls
MQG, best burst damage trinket. Also when your fully buffed (around 900dam) it will outshine even rotd, especially if the fight is around 6-7mins
reed, stable avg damage.

botom line is you will always have to swap around your trinkets.