1) Nothing happens, and I just hand-wave the journey. Encounters only occur in set-piece locations (dungeons, caves, etc) where I can "force" a certain number of encounters per day. But that limits my ability to tell a story. Lots of classic fantasy tales feature "events on the road". Unacceptable.
2) Sufficient encounters occur over those four days so that the balance guidelines are met. That means 16-20 combat encounters just to travel 100 miles between Town XX and Ruined Keep YY. That's incredibly boring. It'll take my group four sessions (four weeks, real-time) just to get to the Ruined Keep. Also, it ruins the story just as much as having no encounters; the journey to the Ruined Keep took four times as long, and was four times as dangerous, as the Ruined Keep itself.
Except if your problem is "blow all resources, long rest each day", then all you need to do is have the
possibility of multiple encounters in a day. It only has to happen one time that the party blow all their resources and then get attacked, and they'll take the lesson (hopefully).
It's also not like this is a new problem: overland travel was only ever a problem in any edition if you were massively out-powered by what you met on the road, which leads to your issue of "dungeons are less dangerous than wilderness".
Finally unless you're totally denying any and all rest in the wilderness, then you haven't really fixed the problem. You've made it so that all short-rest powers will get burned every fight instead, while everyone with long rest powers just kind of hangs back.
I think there's a couple of problems that cause the 5-minute workday.
Exhausting resources is risk-free.
This applies in the wilderness or in a dungeon. In the wilderness, it's caused by wilderness encounter guidelines and itineraries that were always flawed for anything except extremely low levels because they were designed to produce a single encounter or event per day. In dungeons it's typically caused by static dungeon layouts which assume that monsters never move around - in previous editions this was semi-decently handled by random monster rolls done on a per-turn basis.
There is no time pressure.
On a short rest basis, this is caused by dungeons being self-contained and extremely small. If you hit the kobolds or goblins, odds are you'll find that every single one in the area lives within the lair, every one of them are currently IN the lair, and their numbers are on par with the smallest of small villages. That means that if you assault the place and leave, every kobold you kill is one you don't have to face when you bother to come back. If, instead, humanoid monster population densities line up a bit closer with real hunter-gatherer population densities, then if a kobold village is threatening a road that's 1 hour travel away, it probably has more than 100 kobolds within half an hour's travel of the middle of their territory. If you short rest before you polish off the settlement, you just multiplied the defending forces by a significant factor.
The only time you should be free to short rest is if you're hitting a complex that is explicitly self-contained AND is entirely static, which basically cuts things down to "holes in the ground filled with unintelligent foes".
On a longer term basis, most adventures progress 'in the nick of time', or are entirely driven by the PCs. The antagonists just sit there, gormless and waiting for the PCs to leisurely wander in, wreck their plans and wander off with a clue guiding them to the next adventure locale. It's a rare adventure that has a calendar of events, and a rarer one still that has the PC's actions actually matter. Even something like this will make short rests less palatable: if you short rest after each encounter, 4-5 encounters (in a static dungeon) takes up a whole day with only time for a short stroll to and from the dungeon. If you short rest once at the end, you can probably knock over the place in an hour and be home in time to head out to the next section of the plot in the morning. That should matter: the bad guys should still be scrambling to get information about what went down. Heck, they might not even know there's a problem. But most campaigns would reward the PCs for making haste from dungeon A to dungeon B with... nothing.
Seriously, when was the last time your PCs made haste to the scene of the final ritual and found the bad guys hadn't even arrived yet? That should be the effect of taking
one less short rest.
]
