The logic is sound, but as you extend the idea, the group starts selling access to their doctor, and you basically pay a subscription for a doctor, and then you just have insurance by another name. It wouldn’t be corrupt like modern insurance, but that’s just because it’s new, not because it won’t get there, unless specific steps are taken to prevent that.
Really, the only thing thatt actually accomplishes here is you’ve removed profit and CEO nonsense from the equation. A community that implemented and organized all these potential communal services would just be a commune. Nothing wrong with that at all, we need more communist principles in our lives.