For someone that's an EH nut, surprised ya don't have Blood-draining over Mongoose.
The problem is that you haven't proven anything or correctly explained anything yet. Reducing the amount of healers, including tank healers, doesn't mean you have to increase your EH at all. Healers with near-full mana bars at the end of the fight most likely were not even healing to their full potential. Dropping a healer allows them to operate at their full potential, unless they're just lazy. Besides, even by your own admission from your examples of EH vs agi, the point of EH is survival by just relying on yourself, not external factors. Removing or adding a healer doesn't change your EH values at all.
I was trying to avoid extreme examples, but at this point I believe it's necessary to help educate you (lengthy post incoming):
Effective health is calculated based off of armor/resist mitigation and health values to give you a grand total to what your HP really is without any mitigation factors (
does not factor in avoidance). Basically, it's a calculation of how much damage you can take before dying w/o heals (aka, burst damage). EH does not have much value for damage over longer periods of time, because either you're getting heals or your dead from burst.
Example time: Let's say we're on ToGC25 Anub, and we have one tank taking care of all the adds. We could go one of two ways.... EH or avoidance. If we go EH, we can stack as much armor/HP/Nature Rez as gear allows (a bear tank could pull this off, most likely). If we go avoidance, we can get to the point of having an "unhittable" tank (like with a warr or pally), so you're basically blocking or avoiding all damage except Leeching Swarm in P3. Which tank do you think is preferred if there's an option? The "unhittable" tank most likely has a very low EH (since it does not calculate avoidance!), but that tank is much easier to heal and more likely to survive
without a heal. The "unhittable" tank could potentially increase their EH at the cost of avoidance, but that actually
increases their chances of dying!
Alright, let's throw those tanks into another scenario, and for ease of example, let's say ULD 25man "Steelbreaker, I Choose You!". We can throw that high EH at Steelbreaker once the other two adds are dead... Fusion Punch, BAM! Fusion punch dispelled, you survived that huge hit w/o a heal. Now we can throw that unhittable tank into this situation... Fusion Punch, BAM!... tank was one-shot.
So what's the point of these examples?
Effective Health is excellent to stack
if you need to survive burst damage or a really big hit. As seen in the examples, EH can either save you or hinder you, it's very situational.
Most people confuse EH with TTL (Time-to-Live) calculations. TTL is simply a calculation of how long you can live without a heal over time (this includes avoidance). The reason more people don't gear around TTL is because it changes on a per-fight basis, since it uses factors such as avoidance, boss swing timer, boss damage, and anything you can do to extend your life not included in EH calculations. If you gear for fights that don't have large burst
you cannot avoid, TTL calculations are much better than EH calculations.
Here's the punchline:
The best way to gear for fights is to make sure you can take the big hits while minimizing damage you do take over the course of the fight. Some people will jump up and say "So that means I should maximize my EH and TTL!" Well, there's the problem: the two examples I've made were Maximum EH vs Maximum TTL. As we've seen, going to the extreme is bad for both depending on the situation, so we can conclude maximizing just EH or TTL is not the end-all answer for tanking.
So what is the answer?
A mix of both, obviously! Sounds complicated, but it really isn't. First, let's get our EH to the point where it's still useful. Bring in Festergut once more... 30k hits, I can gear over 60k health and take two hits... I can't get 90k health yet w/o cooldowns... alright, let's gear my stam/armor values around being able to take two hits w/o a heal. Next, let's get our TTL maximized around this EH we have selected for ourselves. How do we do this? Keep yourself at your pre-selected HP (in this case, we chose 60k) while increasing your avoidance where you can. Does this mean I just gem exclusively avoidance?
Surprisingly no, you can still put on some more HP if you choose (I don't fancy being at 1 HP after two hits anyways), but favoring avoidance gives you a much better chance of living w/o a heal.
Let's go back to your statement about needing to increase your EH if you drop a healer or a healer dies. If you can still take the burst (as in you've tailored your EH to do so) before the heals come in, will increasing your EH keep you from dying? Well the burst is gone, so you're more concerned about living longer beyond the burst, so increasing your TTL at the cost of EH is the best way to go. Yes, there is a balance: don't increase your TTL so much that your EH cannot survive the burst (with our Festergut example, don't drop so much stam in favor of agi so that you can only take 1 hit instead of 2).
Phew, that was rather lengthy, but if it helps educate the bear community, it was worth the time! This is basically what enigmaran was saying (took me so long to write this he responded before me), just more in depth.