Above and beyond all else I would like to see the end of the 5 minute work-day by making all classes based around short rests. Every class should regain class features on a short rest.
It's not a good idea, as others have pointed out.
If all features recharge on a short rest, then everyone is encouraged to "go nova" on every single combat encounter, and take a short rest afterwards.
This forces the DM to have more or less all encounters the same difficulty. The idea that on a given day the PCs have a variety of encounters between the easiest ones, which consume few resources, and the hardest ones which prompt the PCs to activate their most valuable abilities i.e. the "dailies" which won't recharge until next day. You potentially eliminate one good resources management aspect of the game.
Gaming groups which practice the "5 minutes workday" are very few. In fact, the idea makes the adventures suck big time and those who fall into this trap generally learn by themselves that it's not fun. Anyway, the reality is that adventure pacing, variety and inherent unpredictability all make the "5 minutes workday" strategy unfeasible unless the DM purposefully makes it possible.
In other words, I believe that the "5 minutes workday" problem is a myth. It exists only in theory, but no gaming group is dumb enough to allow this to keep happening on the long term. It can happen occasionally that the PCs can manage to take a long rest just before the BBEG confrontation to maximise their chances... and what exactly is wrong with that? It is in fact part of good planning, but it is still subject to lots of uncertainties.
I'd rather eliminate the 5-minute workday by using the rules for "gritty realism" in the DMG. Short rests = 8 hours, Long rests = 1 week. Resource management becomes a lot more important, and natural healing makes a little bit more sense. The decision to "go nova" in an encounter becomes a lot more important, and not to be made lightly. The party will be a lot less likely to take a long rest after each battle if they know it will cause them to fail their mission (or die of old age).
Indeed, your suggestion to go the opposite direction does in fact have a positive effect on a group tempted to take too many rests.
Normally, a day-night cycle is enough to prevent the PCs wanting to call it quit too early, because a lot of stuff can happen around them in a day, so that they cannot normally afford to just wait until tomorrow before continuing their quest.
Your idea means that calling it quit to regain all limited abilities is simply a no-go, as it means that the rest of the world has potentially up to a whole week to go on with their business, likely making you botch your quest. It might still makes sense for the PC to wait a whole week in the slowest-possible paced adventures, but generally it will mean that 1-week long rests are taken mostly between adventures, during travelling, or (if the DM considers this light enough activity) while investigating.