I'm at around a year of playtesting at this point.
In my experience, the PCs take short rests when they have to. If a battle is particularly tough, if they triggered essentially three encounters in a row without a moment's rest (because of the noise they made during the first and second), they are exhausted at the end. They need to spend hit dice, re-memorize spells, etc.. So they go to a place that is safer, they bar doors and lay traps and caltrops and alarms, etc. to arrange as best they can for an hour of peace, etc.. Due to wandering monsters this does not always work, but it usually does.
If they take too many short rests, the odds catch up with them on the wandering monsters, and it goes wobbly. So, the game seems to allow for "just enough" short rests to keep things interesting without making it a short rest after every encounter. Sometimes they squeak in an extra short rest when perhaps they normally would not, and sometimes they get caught resting when they should have been able to pull a rest off, but on average it seems to work out pretty well.
There seems to be a natural balance they reach, on average, thanks to the combination of wandering monsters and exploration and investigation that goes on in our average adventures along with the combat. I cannot put a precise number on how many it is a day, as it always varies depending on what they are doing and what they are encountering in that area, but I think the system as written deals pretty well with this issue without the need to worry it will be too few or too many short rests. That is, provided you stick to the exploration and investigation and wandering monsters suggestions that are pretty prolific in this edition.