Free your game from the D&D paradigm of magic. It's too limiting.
It's less about the paradigm of magic than it is about the paradigm of conflict in action-adventure generally.
In one game design thread I read back in my TBP days, a poster noted something that has stuck with me ever since: The biggest problem of RPG combat is that two game elements the target audience strongly likes -- (a) frequent combat and (b) realistic-seeming combat -- tend to logically lead to a third element the target audience strongly
dis-likes, i.e. (c) frequent character death. Cheap and easy healing is only one way to get out of this bind -- some games try to teach players the hard way to be much more careful about fighting than usual, while others will deliberately structure it to be far less dangerous in practice than the fluff implies -- but games which have
no way out of that bind tend not to do too well.
So if cheap and easy healing isn't available to characters, the game either has to be tailored to make its absence less disruptive, or the group has to get used to what may be a very different playstyle -- which, again, as you rightly spot, is a case of one player's concept changing the shape of the game for the whole group. That a good many groups will have no problem with this, I don't doubt; it's the presumption of the moral authority to
demand it that I, like I suspect a number of others 'round these parts, object to.