Well... for one thing, I would argue that AST is the least DPS focused of the healers. It's numbers aren't bad, but everything besides the DoTs are a touch less powerful than WHM spells. However, as AST has less burst healing, this translates to less time available to cleric stance, and an AST needs to juggle cards on top of that.

Now as for the core content of your post... There is one fundamental flaw is is why (I think) it's unlikely to happen.

Rotations for DPS are OK because, while occasionally burst is needed, for the most part it's averaged out over the whole encounter and that long term average is what really matters. HPS, however, is a useless stat... players have tiny HP pools and being even a little behind on heals means death. Healer kits are 100% situational and with good reason: you never know when someone might eat a bit of avoidable damage, or the boss might get a crit streak on the tank, and so on. Or if a mechanic punishes the party with vuln stacks, the healer needs to step it up in generally.

For Warrior, a stack building system works because tankbusters always happen at specific intervals and generally never closer than a minute apart. Raid hits, however, can be spammed and hit hard and outside of tankbusters, there can be spikes of simple auto attack damage as well. Add to that that different encounters can have very different patterns of incoming damage/healing that aren't built with having a rotation in mind.

Of course, it would really depend on how optional the stance swapping would be. If the healer could completely avoid using the ability that results in a stance swap, maybe not such an issue, but if heavy damage would effectively force it... That might be.

(15% def buff from every heal would also be slightly OP)