You do realize that most healing spell take more than 2 seconds to cast ... right? Especially the spell that potent enough to keep a tank who is melting alive. Meaning even if the healer somehow starts casting moment before you even get hit, you still won't get the heal in time anyway. Sure, there is instant cast, but at lvl69 they are basically oh shit button reserve for an emergency, not the tool healer are expected to use when the tank has a single group of trash on him.
Even if we assume the healer gonna spam their faster heal, it will requires them to react within just half a second of you getting hit to get the heal out in time, something that ... unless I misread ... you proudly claimed you can not do yourself in the following quote:
yet you expect your healer does?
I don't know if you realize how entitled or oblivious you are to your own problem. You think it's perfectly fine for you to make an excuse that you die too fast to active your mitigation ... which would be an instant cast ... yet you think it's 100% reasonable to blame the healer who would have to also hit a button - with cast time - to heal you up in time? Do you even realize the absurdity of your logic here?
Also, in your own word you admit you die in just 2 second with MINIMUM amount of trash on you, that's 101% on you. At proper gear level, a tank will easily last for more than 5 seconds even if he pulls wall to wall. And your recton "I did it later with another healer" doesn't mean anything positive for you, it just means you being carried. Claiming you don't need to be carried doesn't change the fact you had to be carried. Clearing a duty is like feeling a jug with water, as long as the needed amount got poured into it, it will get filled and the duty can be cleared, that doesn't mean everyone put in their fair share. The fact is simple, it's impossible for your to contribute a fair share with the gear you had no matter how much you want to dress up your argument, that means your group had to compensate for you, and that means you were being carried, and no amount of self-protest will change that.
I'm glad I see a lvl80 BRD attached to your avatar, and I hope that's what you will stick to. Don't get me wrong, it's not even a matter of skill. Every one was no0b once, I had been kicked both as tank and as healer before over my many years for being bad, for trying to sneak a clear without proper gears ...etc... the difference is I realize when the issue lie with me. Based on the way you tell your story without realize how absurd it is, and the way you response to people ... I'm not sure you can do the same.