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
Kingmaker has a punitive resting mechanic that could lead to a game over. That's not really what I have in mind.
I said 10 but I could have said 12 or 14. It's more to give an idea than to suggest a value.
I really think a balance could be found to make resting more meaningfull while preventing at the same time players from being stucked.
You’re talking about PoE (and I agree that it was boring) but I find Solasta to be a better comparison.
Despite the fact that the map design is linear in Solasta, BG3’s map is also divided in area with a starting point and an end. The end may be different but it does not change that the area is “done” and that you have reached some kind of “checkpoint”.
Supply bags could be a reward after you reach those checkpoints whatever the solution you have choosen.
The restriction should definitely be balanced. It should not be too restrictive but we should not always have 3-6 supply bags ahead in my opinion. It clearly gives us the message that long resting, managing and using wisely your actions/features/spellslots does not matter.
The player should not be the only one to determine when the day is over.
Ultimately, what is the importance of food if you can buy unlimited quantities from a merchant?
Well, what is the importance of food now ?
Extremely easy to long rest or extremely to long rest without having to look for food if you plan to long rest 40 times during act 1, I guess.
Food just needs to be a little more scarce, and come more from combat/questing and less from barrels. I don't think they need to completely overhaul the system.
The goblins camp contains enough meat for you to rest the whole EA. Should they remove the barbecue ? I don't really think so.
I think they should give food a value of "0 supply" for players who wants to be challenged by the game's core rules
