Alot of tanks also get used to the idea that healers will use cooldowns to save them.
Divine Seal, Presence of Mind, or sacred soil/lustrate, eye for an eye, even shadow flare to slow mobs, etc.

These are tools that healers have had to help with spike damage on a tank. AST do not get any tools to handle burst damage well. The only options are a Benefic2 proc, Essential Dignity, and using an Arrow Card on yourself. These don't even come close to the effectiveness of what real healers get.

Tanks need to learn to be more self-sufficient with cooldowns. AST are fun to play, but their healing throughput does feel very hard-capped, and if a tank exceeds that... well, you've seen it already.