It could be cool yes, definitely.
Here's a suggestions of supply bags locations to suit this suggestion.
I think 10 supply bags (+4 through merchants) for act 1 is not too restrictive but is restrictive enough to ensure that players are careful with long rests.
Just to give an idea, In my last playthrough when I reached the grove I had 6 supply bags !
From experience I can say that there is a good chance that it may not be enough, but maybe rng doesn't like me
In general, limited food is quite dangerous because it will look different depending on the team composition, player knowledge or stupid rng.
It is impossible to make a "meaningful" rest that will also prevent the player from getting stuck (which the game should not be able to do). RPG games are so long that after such a blockade the player will most likely abandon the game.
Kingsmaker had a meaningful rest and eventually found most of the players didn't like him very much.
In the end, rest will never matter (unless Larian introduces some commonly disliked mechanics), at most there will be half measures that will only make the game more irritating, such as supplies in PoE
