If you risk dying to that one wyrm tail then you should either cd there or let your healers know to not let you drop too low. Tank survival is both your job and the healers', there's no such thing as "I just cd here and there, and if I die elsewhere not my fault" and if you want an optimized (not tank catered) run, you need to let your healers know what cds you're using and you need to know what heals your healers use on you. If you don't have enough cd to mitigate then ask your co-tank to cover or do tank swaps when needed. Let your dps know too if you want palisade/apoc/feint/addle/minne at specific times. Those are mitigation tools as well.
I honestly don't like the saying "if you die to autos your healers need to be replaced" since it oversimplifies things too much. Your healers may expect things to go differently, like eos healing the tank or the tank surviving long enough until charybdis since they'd drop to single digit so having high hp before that would be a waste if the tank could survive without a heal. If your healers never let you die to stuffs then they probably haven't found their limits yet. I'm sure whoever came up with that saying was half joking or didn't mean it to be taken literally.