DPS can still be important without hard enrages; and you can still have hard enrages, just set them at 15 minutes instead of 10 (assuming the fight is balanced around 10 minutes).
To do this though you need Healers to have finite MP, and have enough unavoidable outgoing damage from the boss that Healers will go OOM within 10 minutes... unless of course you use mitigation, and party MP regen abilities, and do mechanics well (death is a huge waste of MP), and debuff the boss, and kill the adds quickly, and etc.
This creates a much more even and natural balance between DPS and Survivability; i.e. if all you focus on is DPS then you had better do it damn well because you aren’t going survive for very long. If, however you focus on efficient survivability (and do it well) then DPS isn't so much of an issue because you can still beat the fight even if it takes you 14 minutes.
Note 1: This would probably require some adjustments to current Tank DPS (Healers should be too busy healing to do much), with Tanks having a greater focus on mitigation.
Note 2: This would require a redesign of Healers (which is probably needed anyway) as current Healer design is too focused on burst healing. Heals would need to be (generally) less powerful but more efficient, including via interactions (e.g. Medica II HoT increases Medica heals by 10%).
Note 3: Set DPS checks are still fine in small doses, so you could still build them in to prevent full Tank / Healer parties, just don’t make the entire fight a hard DPS check.
Note 4: Soft enrages could also be used, and start around the 10 minute mark, with each ‘rotation’ getting harder and harder to survive; this would create a ‘standard’ finishing point that you would want to aim for while still allowing variance in party composition and approach.
... Either that of SE needs to fully embrace the DPS nature of its designs and give Healers a decent damage / support kit.