I'm bored when I heal because I need more complex DPS rotations

[Anxin]

So instead, I've taken to asking a different question: What other modern multiplayer game has a healer/support role, where they are specifically designed to ONLY heal?

I'm uncertain if you can call it modern, but Guild Wars 1 often required the solo healer to only heal and support. You were too busy doing that to do anything else! Even when there were two healers/supporters you were too busy throwing out heals and buffs and debuffs to worry about damage. And all of it without scripted AOE dodging and other things. The admittedly simple AI kept you alert, in part because healers were the AI's primary targets for debuffs and sudden damage spikes. Honestly, I miss solo healing for parties of 8.

The FF14 healing kits are powerful enough that you often don't need a cohealer. I've switched from healer to dancer and that class has enough healing for a team that plays well in casual content (just a small boost and another healing skill would make the class a pretty solid healer in its own way).