Short rests should be unrestricted, but you can only heal for whatever hit dice you have remaining. The amount of hit dice is going to be your real limiting factor for the amount of rests you can take. If you have no more hit dice left to spend, you don't get HP back. I'd also ideally like some setting to decide the number of hit dice to spend. Maybe I didn't take any damage in a fight and want to save them. Maybe I took a lot of damage and want to spend more than one.
I'm not sure there are time-restricted quests, or that time advancing exists other than main story beats, so asking for time to advance may not make sense.
The problem with unrestricted short rests is the Warlock-type classes that regain most/all of their abilities/spell slots/dice back on a short rest. I mean, my main is a 'lock so I'm ok with that, but it makes the game esaier if you can do that.
2 per day, as mostly everyone has said, is truly the optimal amount, otherwise you can have a party of warlocks and battle master fighters and just cheese the game.
