There definitely needs to be some restriction or disincentive to long resting at will, otherwise classes balanced around Long Rests will be more powerful than intended, which isn't good for those balanced for more short rests.
...But any consequences can't be too impactful, like advancing the tadpole progress, because then people could get stuck in an unwinnable state and need to restart the entire game.
Solasta does this currently by having rations be the resource consumed... but that obviously won't work if you can stockpile tons of rations.
I couldn't agree more.
Short rests should be available whenever you're able to take a breather, not just once per day. The D&D 5th ed. rules as written place no limit on the numer of short rests a day and mandate a duration of 1 hour. Many DM's have house rules reducing this even further: Matt Mercer of Critical Role, for instance, allows his players to take short rests lasting only a few minutes.
It used to be half an hour, but he's been much more of a stickler to that, and enforces the one hour rule pretty consistently these days.
I think 2 or 3 short rests per long rest is good.
Long rests, conversely, should be available only once per in-game day, and it is crucial that there be real, tangible consequences to the in-game passage of time, so players don't just blow all spell slots every fight.
What's an in-game day? Time doesn't really pass noticeably. There is a state "Too Soon For A Long Rest", but what conditions should allow that state to progress to "Can Long Rest Now"?
It can't just be completing quests and objectives either. If the trigger is complete 3 quests, the map has 6 quests and you are able to complete 4 of them well enough before you need a long rest, and there's only two left, but one is tough enough that you need a long rest before you are able to do the other one, you're stuck because there aren't enough to do another long rest.