As an up-front: I have not played SCH at high levels; in fact, my mains are the other three mages (WHM, RDM and BLM). Excluding RDM, the other two mages work fairly well in Abyssea now; WHM is where it should be, at the forefront of healing. BLM is, well, nukes still aren't nearly powerful enough to keep us on par with melee, but SE won't ever fix that. At least yellow procs make BLM useful.

RDM and SCH, however, are obviously still broken (within Abyssea at least); SCH has got to be in the worst shape out of that pair. From my perspective, however, the problem with SE's vision is that it's still assigning to SCH a kind of "in between" role. Good at both WHM/BLM style roles, but excellent at neither. And if there is one thing the player community has cemented fairly well over the years, it is that jobs that don't excel in one particular needed aspect, almost never get invites. It is with this in mind that (and this is half-directed at SE's development team) I propose SCH be given a new vision, something unique that it does that no other mage job has much access to.

TP and enmity manipulation would be a possible area, as mentioned. I think Enhancing Magic is probably the only category to really go with. Obviously Healing is a WHM's specialty; Enfeebling (should be) a RDM's specialty, and Elemental is for BLMs. Any attempt to make SCH relevant in those areas would almost by definition destroy the respective main jobs listed, for SCH can provide a lot more peripheral abilities than the others. That's what has made it so hard to buff in the first place.

Enhancing, though, is ripe for some new abilities; you could have on the mage side some Fast Cast bonuses, perhaps. You could give them some spells that mimic certain MAB bonuses CORs currently provide (but not to the extent of COR, likely). And yes, some sort of Regain spell perhaps, or a spell version of SAM's TP transfer. Some enmity manipulation spells, not just monitoring. I think this is probably the best route to go in for SCH.

TL;DR: I have trouble with the idea that SCH should remain as a magical generalist. It hurts their invites, and any attempt to power them up enough for this not to be an issue, will almost by definition destroy the balance with BLM or WHM. As long as Abyssea remains the end-game, "efficiency" is thrown out the window, and thus SCH hurts. They need to go in a new direction. Since RDM should be receiving some buffs to maintain its status as the elite enfeebling mage, this leaves only one real area to go to: Enhancing. Yes, it competes with BRD and COR, but there are still a lot of ideas they could throw in that they haven't used yet to give SCH a nice niche. Just my two cents, anyway.