If I'm misunderstanding please feel free to call me out but I think what the OP is asking for isn't more "hardcore" content necessarily but just content in which tanks and healers have less time/freedom to DPS. Even in Savage/Ultimate tank and healer DPS is very much a thing that is expected, more difficult content doesn't necessarily mean more tanking and healing but just being more skilful with their application.

From a healing standpoint I think a lot of my freedom to DPS comes from the scripted nature of a fight, especialy on SCH and AST but also on WHM to an extent. Adding randomness to an encounter could easily make certain bosses require more attention and specifically topping off health bars because as it stands right now there is a ton of time I'm happy to leave a full party under 50% because I know nothing awful is coming and I might as well wait the ten seconds for Thin Air to cone up to cast a Medica II and save myself 1600mp by casting Stone instead.

This sort of play is encouraged but wouldn't become possible if there was the potential for unscripted raidwide damage, though cast bars could still give a bit of warning.

There is very little else that I can think of to add healing necessity that wouldn't exclude the even-more-casual-than-me players without also being really arbitrary in nature like oneshot mechanics and consistant HP degradation that would force an HPS increase.

For tanking I have even less to say.... More enmity resets? Remove enmity mitigation from other roles?

Again there are certain things that could increase the necessary tankiness of a tank (stacking vuln up becoming really frequent, nerfing AoE enmity generators) but this feel like arbitrary difficulty increases that would just serve to force someone's hand instead of making tanking engaging. Maybe something where you can only hold an enemy for so long/have so much enmity on it before it hits a sort of tiny "enrage" and does big damage (think Temple Bees) or goes to poke someone else because it's bored of you?

I dunno, excuse my ramblings. I think these things could be fun though, thanks for making this thread.