Orcus on a bad hair day
But this solution is that most of the players still don't care, and one player has to care - and carry - everyone else.I played entire campaigns without a cleric, back in 2E, so they definitely weren't mandatory. It did create a different style of play, though. You wanted to avoid taking damage, since it would add up so quickly.
It may seem like an extreme, but given how far things have swung in the other direction with 5E, I find it much preferable. I hate the idea that you need multiple combats every single day, before anyone starts to feel it. I hate the idea that you can take a few arrows and simply not care, because you were never close to death and you were going to heal up to full regardless.
Truthfully do you think that at an average table if there were characters with access to healing but not intending to use them the rest of the party would not pressure them to spend those resources (spell slots, whatever) to heal them up? You're making that a class that can be healer will be peer-pressured into must be the healer in the majority of groups.