I wouldnt eliminate any of these things from the game completely just find a way to make the less common so less accessible to players. The less they can just get healing magic and magic in general on a whim it may make them consider how theyre going to have a party member healed, cured from diseases, regenerate lost limbs, etc. If they pledge fealty to a patron or church, it might make them a better party. As I said above there are some problems with the group dynamic so Im giving this thought as a possible solution.
I think you are already aware of what to do and not to do, and you are focused on the positive aspects of your campaign decisions.
So I am confident that even if you go hardcore and just say "no spellcasting PCs", you'll do fine.
The need for HP healing is dependent on how many combat encounters you have per day, so the DM can just plan adventures accordingly, by spacing the encounters more across multiple days or even farther away in time. This can actually help against the "I have more levels than years of age" syndrome.
Non-HP healing is also not as critically required as someone may think. Yes, there are monsters and spells which cause paralysis, poisoning, blindess etc. but most of them are temporary effects that will go away before the next encounter. No restoration spells for an immediate fix? Good! Finally those temporary effects will mean something and won't last less than a round
Resurrection? That's not normally something you have until higher levels. Ok, there is revivify already at fairly low level, but once again this is something dependent on the combat encounter rate per day. If someone sees revivify being used regularly in their game, and you take the spell away, again reduce the number of daily combats i.e. space them out more across different days. And by the way, we've spent years talking about how resurrection spells are almost a cheat, how to mitigate the triviality of a Raise Dead by requiring a quest instead of a GP price tag... so I don't think we should worry about missing resurrections capabilities in the game.
And maybe, how about just letting the PC die once in a while? PCs don't want to die anymore these days...
All in all, I think you should try out this sort of campaign without worry. Think of it as an opportunity to learn more about the game, the worst that can happen is a TPK... and what exactly is a problem with one of those, once in a while? Maybe it'll be something that will make you all laugh around the table and put some spirit back into the group. If the experiment doesn't work, it's not like you have to stick with it for the rest of your days anyway