Well, what would you define as burst healer?
All 3 healers can top a party from 10% to full in a few GCD
I think what people mean by burst VS HoT would be that most of the heal actually come from the HoT portion. A bit like MedicaII with a stronger HoT and weaker initial heal.
However there's very few case where MedicaII HoT will actually heal on each tick over its duration.
As a side note, HoT doesn't mean it has to be a really lengthy weak HoT. (like they all currently are in this game)
HoT can be powerful, most HoT from WoW's resto druid have a rather short duration and some of them are actually tweaked to make most of their heal in the initial ticks.
But something like this would require FF14 to rework their ticking system.
And yes current, current healer are tweaked toward direct strong heal. (what most people could call burst)
for AST/WHM, their basic heal are a simple yet good example. cure1: small heal, cure2: bigger heal, most ofgcd are also quick hp recovery mechanic. Essential Dignity, Assize Tetragrame etc. They are all based on giving hp quickly.
There are few other options, Asylum and Collective Inconsciousness, but seriously, how many time will Asylum actually heal on each of its tick (unless placed on tank) and since when do AST use C.I for the HoT? C.I is almost exclusively used to reduce a boss aoe burst, the HoT is then useless as more often than not the other healer will cast 1 or 2 aoe heal topping people (and if they aren't the HoT will perhaps tick once or twice and that's it)
If mana was a concern perhaps healer would be more kin to let HoT ticks. But mana is far from being a concern since not only we have more than enough mana to spam almost anything + rez 4-5 time a fight, and on top of that we have so much of it that we can actually spamm the boss with dmg skills.
So beside optimising your dps on a fight you know very well (so you know when you can let HoT ticks without risking a death), there's no incitive to let a HoT tick.
Most player will simply spend another 2sec on another Medica to be sure everyone is full.
And this is possible because our heal are just too potent. It is simply too easy to top a group.
So this is why Ithink, most people say "it wouldn't be really good" when it comes to raid wide damage is that most fight do ask you to heal quickly the damage.
Very few fight leave you with DoT slowly crippling you or anything making a HoT useful. And when they do (like shin) the DoT is so weak that you barely notice it.
So far only tank benefit from HoT and since most fight only require 1 tank a time for a significant portion of the fight, it's not something you'd value the healer for.
Group are more concern by the lack of shield than the lack of HoTs. If you go as double WHM, you're worried that some aoe may kill one of your dps. Going as double shield is more an annoying than anything else, but this is easily fixable by making one healer not applying shields.
And this is also something they'd need to adress.
Assuming they do make some kind of HoT healer, it means that you could end up with a shield less group (unless they'd give shield to all 3 healers but WHM, that'd be odd), fight would need to be designed around that, and they are currently not designed around not having shields. Unless you overgear the fight, many boss will simply obliterate dps and healers on their first AoE.
Well that's fine; I'd probably stay with my AST too but many player would like to play a HoT healer and this is something they don't have access to. (and no, WHM isn't a HoT healer, having access to Recup + Weak MedicaII HoT doesn't make you a HoT healers)