1. Do not touch Tanks' self healing. Let tanks be self-sufficient to some degree. It does not feel good having to rely on your healer for the vast majority of your survivability as a tank. Dieing a death of a thousand paper cuts as your health is chipped away and you have no way to recover. Meanwhile your friendly glare mage is busy giving a dragon nasty looks as you lay on the floor dying.
2. Make healer's DPS more complex. We don't need to be DPS levels of complex, but we can have more to manage than a single button, a DOT, and MAYBE one button you hit on CD for a slight bump in DPS.
3. Consider maybe adding more unavoidable party-wide damage to the game that needs to be managed.
4. Consider adding mechanics that require healers to pay more attention. Perahps periodic debuffs that need to be healed through or dispelled that cannot be mitigated through other means. For shield healers, consider debuffs that will apply to the target if damage is done to health, but do not apply if damage is blocked by shields. There are a lot of ways to make healing more engaging without making stripping tanks of their agency.
4. give us hard mode versions of old dungeons that we can queue for for increased xp/rewards. These should slap the party around, forcing the healer to stay on their toes. Tank healing will help to ease the burden, but will not suffice on its own.
I make this post as someone who plays almost exclusively tanks/healers.