I've been following the AST discussion here and elsewhere since the beginning, but haven't chimed in yet here. I find that my experience closely mirrors Kayleen's, so this seems the best place to add my two cents. I wouldn't consider myself hardcore, but I have been healing in MMOs for over 10 years now. Our somewhat laid back raid got our first A1S clear last night.
I, too, was pretty excited about AST when it was coming out. I love the style and concept and after almost 2 years on SCH, I was ready for something new. For me, the first sign of trouble was actually before the release of Heavensward, when they announced the two aspects. I wasn't surprised, but I knew that meant that instead of creating a new unique healer, they had taken the easy way out for keeping things balanced.
My healer partner plays WHM, so when we started A1S, we were running WHM/AST. For whatever reason, my healer partner is never comfortable solo healing advanced content, so it ended up falling to me to solo heal phase 1 on AST. I have to say, solo healing phase 1 is quite tight on AST. I tried it on both Diurnal and Nocturnal. No surprise, it's probably easier on Diurnal than Nocturnal. I feel like solo healing on AST in phase 1, there is very little room for error, you need to get those heals out during the prey just right. I definitely think it's possible, but it felt inconsistent. As for the phases after that, I don't think I had quite enough practice to fully get a feel for the best way to approach healing during double prey's. I think it's about the same as solo healing phase 1, possible, but with very little room for error. More importantly, as many have pointed out, running AST can shift a lot of the burden to your co-healer. I think this means that it takes a little longer overall to learn and adjust to the healing for the fight.
Anyways, my static, and critically, my co-healer, wanted me to run scholar after that. The difference was clear. First, Faust was much easier. It wasn't that AST DPS was bad, but I could DPS longer with SCH because the fairy was helping to heal the tank, and that made the DPS check far less of a problem. I shudder to think how many of our 1-2% wipes could have been clears if I had run SCH that first week. That also had an adverse effect on use learning the Oppressor fight because we wasted large amounts of time with Faust.
On SCH solo healing the first phase was not an issue. I had to adjust to prey a little bit, but once I got that down it was fairly straightforward. Essential Dignity is nice, but having the Lustrates for the rest of the fight was even nicer. Also, things like Eye for an Eye and just healing from the fairy were quite welcome. I also felt it was safer to hop into cleric stance and do some DPS on SCH, though I'm not sure if the DPS I did amounted to more than the cards would give through boosting DPS.
Bottom line, SCH was more secure, and it allowed us to spend more time learning the fight and less time dying in frustration (we still did plenty of that). Yes, AST can clear the content, but the window of error is much smaller and your co-healer has to be on board as well. I can also understand why some savage groups in PF might want to exclude AST. When the healers are strangers, you probably want to take the safest pair into the instance. Now that I've gotten the clear and have a higher comfort level with the fight, I think I could get through it on AST, but I'm not sure if my healing partner would be on board.
There have been many suggestions on how to adjust/fix AST, and I, of course, have some of my own, but it seems to me that WHM/SCH is generally a safer option, and I think that's going to make it the go to choice for people doing progression and people in PF groups. AST doesn't have to bring a huge advantage compared to the other healers, but it can't be a liability, and for many groups right now, I feel that's exactly what it is.