I find a DoT centric job to be unlikely.
They didn't strip existing jobs of their DoTs to make room for another one, they did so because they're a pain to balance and because too many debuffs up at a time causes issues. Frankly I'm amazed BRD still has two DoTs, and wouldn't be surprised if it lost one in 7.0.
One weak DoT that doesn't have 100% uptime is one thing, but when you have multiple DoTs competing with what are supposed to be powerful spells, you run into issues like SMN had. When you're base potency is something like 30, and your only seem to count in multiples of 5, you don't have much wiggle room to adjust your damage output, you either buff to 35 or nerf to 25. Then when you get to your burst phase, your nuke spells can't do too much damage or you end up obliterating everyone else in the damage logs, so you end up with a Burst phase that's weaker than most jobs sustained damage.
The only way I could see a DoT centric job working now is if they have ONE DoT, but they can modify it or have it interact with mechanics in some way. Such as spells that increase the potency of the already applied DoT or spells that deal more damage if the target is already afflicted with the DoT. But that still comes with the 'difficult to balance' problem.
First off, you can't count BLU.
Second, only seven of those jobs have DoTs that you're supposed to maintain 100% uptime on, and four of them are healers so you could say it's a trait of the role. SMN used to be one of them and it had three of them all by itself.
Chaos thrust is 40 potency, Higanbana is 45 potency, and both of BRDs DoTs total 35 potency combined.
It's why, even as the selfish DPS poster boy, SAM's weaponskills are themselves even weaker than NIN's in terms of raw potency. That's not asignificant issue by itself, but when you're talking about adding a job with multiple, significant DoT effects, you're going to end up with individual spells with pitiful potencies, and then when it comes to level scaling and burst phases (#2minutewindow) balance will be a nightmare.