The biggest downside to this is healers are already very high responsibility. Mistime one heal and the tank dies, or the raid dies, etc. If you do this, you're adding yet more responsibility to the role - one more thing healers have to learn, and in high end content, not mess up lest the party wipe. One more thing to juggle, which might be particularly hard on ASTs since they've got cards already.
That doesn't necessarily mean it shouldn't be done, though. One advantage would be being able to plan heals around the mitigation more directly, not having to worry about someone else missing it.
But... just be careful with this one... this is definitely a two edged sword kind of thing.
Physical ranged jobs are like this. They have some traditional rotation elements, but a lot of it is watching for procs and priority based.
My biggest concern with a rotation like this is it would lead to slashing healing abilities. So healing would be even more simplified. I don't want that.
Adding just, for example, a second dot back should be fine though.
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As I think on this a bit more... well, I'm going to be bluntly honest: A lot of healers out there I've seen tunnelvision and kind of suck at multitasking, even just at watching health bars while DPSing. The level of attention that a proc-based rotation requires... well, I think it would make it a lot worse.
Here's where I agree the most. When I'm playing a healer, I want to, you know, actually heal more.
It's a difficult problem to address not just because of stuff like ilvl bloat, but because of the way battle encounters are designed on a fundamental level.
Sadly I don't have a magic bullet solution. Simply nerfing heal potencies won't do it either - SE seems to have dabbled in that slightly with ShB and well, yeah. It's really hard to think of a way to do this without suggesting a total overhaul of battles, which of course won't happen...