The psychological impact of dwindling resources is the atavistic foundation of what is considered 'exploration' in an RPG.
I don't think a type of 'resting system' is necessary but it is one example that plumbs those depths; if you are looking for an easy example of how resource management ties into exploration and role-playing on a mechanical level then look no further than Wizardry 1: Proving Grounds of the Mad Overlord.
This is a very basic RPG concept and any system, be it a rest system or any other, needs to have immediacy and it needs to be either scarce, or difficult/rewarding to achieve.
In Wiz1 it was very rewarding to make your way back to town and the game's inn in order to rest up and refuel in order to head back into the dungeon depths. The further you explored the harder it was to make it back to town and the game managed to imprint real psychological manipulation, the most fight-or-flight responsiveness, thus making player choice something not only real but also tangible:
Will you risk further exploration and possible party annihilation? Will you risk attempting to disarm and open this trapped chest and risk party death or injury?
Will this amount of spells be enough to get you back to town?
Your party has been poisoned, and if each step taken drains 1 hit point and you have only enough potions to cure half your party does that mean you can make it back to town if you cure characters X, Y and Z, or if you cure characters A, B and C instead?
All such basic impetus but effective nonetheless. I don't have any answers as to how that same kind of psychological manipulation can be achieved with a rest-anywhere system specifically because a rest-anywhere system, by definition, requires a more complex attribution of systems interplay and is thus harder to 'balance'.
I do believe, however, that a rest-anywhere system fosters The Path Of Least Resistance, and that is the path where design flows not from the role-playing derived by the game's game play, its classes and characters and resources, but instead the path where design flows from a vague concept of availability instead of limitation.
It is harder, much harder, to 'balance' the lack of a resource than to do the opposite.