The scenarios you describe make the idea of anything other than long rests effectively meaningless...and frequently even long rests. Why would a wizard conserve spells when there is a very real chance that their next encounter won't be for days or weeks?
That is, indeed, the question. The system is balanced with the assumption of a ~6-8 encounter day, according to the Basic DM pdf (presumably the DMG will have the L&L-promised "crystal clear" guidelines as to how many rounds that should add up to, as well - and hopefully something about the expected number of Short Rests). Deviate from that assumption, and you lose what balance there is.
I have also run many many many games like this. It becomes my job as the DM to balance the encounters presuming that the party will be more (or less) likely to go nova depending on that sessions/adventure/campaign's pace.
Encounters, yes, the DM can compensate for 'short' days with harder encounters, dialing it straight up to "deadly" to make a single-encounter day challenging - though that's not always going to be appropriate in a slower-paced campaign.
Class balance is also an issue, though....
In a scenario where encounters may be days apart, any short rest powers essentially become daily powers: When all encounters are 15 to 75 minutes apart, short rest powers gain some value...but there is stress in accessing them. When all encounters are back to back, short rest powers again become daily powers.
Very true. If you can /count/ on an hour or more between combats, Short Rest powers are essentially available in every fight, as well. That's quite a range of possible levels of availability for a recharge-type that accounts for all the Champion's and Battlemasters' limited class resources, and the lion's share of the Warlock's power. Clearly, the effectiveness of these classes could vary wildly depending upon the pacing of the campaign and the ability of the party to make Short Rests happen.
The default assumption for 5e rules is that the party will experience 6 to 8 medium to hard encounters in an adventuring day. The rules behind resting are founded upon that assumption. Any deviation from this will of course create distortions.
Agreed, that's how it looks. Unfortunately, it flies in the face of 5e's "support many playstyles" goal. So far it supports you only if you pace your campaign a certain way - and, they haven't even shared exactly what that one supported style is.
Clearly, we can expect more from the DMG than from the pdf, so I fully expect to learn the prescribed number of rounds and short rests per day, to go with the prescribed number of encounters between extended rests, and the encounter guidelines. Which'll be great, at that point we'll all know how to run D&D without distorting it.
Hopefully the DMG will also have some more robust DM tools to help reduce or compensate for those distortions. Something more than "make it average out," that is.