I would say 3-6 short rests. I think unlimited is abusable with certain class types. But to few hurts those same classes.
I do not think it should be level dependent. The rest system is a balancing mechanism that should function constant throughout progression.
Since the game can't time pressure us or give us complications for attempting a rest, the game has to provide another system to balance resting.
Hit Dice makes it so abusing the system doesn't work. Why? Once a character or 2 are out of Hit Dice, it gets harder and harder to short rest and get anything out of it.
Example:. You're a Warlock, so you get spell slots reset every short rest. Big deal. Once you no longer get a healing benefit from short rest, it's usefulness drastically decreases. You only get 1 or 2 more spell slots per SR. It's not going to benefit you that much if you keep SRing when you have no more HD.
The only class that could spam short rest and fully heal as a result is Fighter with Second Wind. Big deal if the rest of your party is unable to do so. What? Fighter gonna solo the Gith Patrol or hag or spider matriarch? Even Lae'zel and MC Fighter would struggle with that.
The point is, if you limit SRs by HD and no hard limits, it works just fine, and SRs are promoted which means people will use LRs less, naturally, especially if they know they have a ticking time bomb in their heads.