One area that they could probably introduce some customization, at least for DPS jobs, would be choices that allow the character to improve on AoE damage or single-target damage. While players would naturally gravitate toward the single-target stuff for high end raiding play, a choice like that could still have consequence since dungeons (which have a lot of AoE) are still a significant amount of the game's content.

For healers and tanks, assuming they actually rebalance incoming tank damage for the future, the choice between damage/survivability and damage/healing could fulfill a similar role, with the former option being more preferred for dungeons and the latter for raids and trials.

The overall bonuses would need to be relatively small, of course (and some jobs, like BLM, that have both solid single-target and solid AoE damage might be harder to balance here), but something like this would get around the "cookie cutter" aspect a bit, as even hardcore raiders typically run dungeons for tomestones, so these kind of choices wouldn't be strictly cookie cutter.

I'll admit that part of my desire to see something like this largely stems from how awful NIN's AoE is though. It's my main but I almost never play it in dungeons because there are just more efficient options.