There are various things going on here.

Short rests are a mechanical device that returns resources, but you should make the time of that reflect what makes sense in your game.

D&D isn't really a wargame - the players aren't usually a tiny cog in a giant war machine that is being commanded or otherwise pushed by external forces. They're usually a small independent group getting into encounters on their own time. Travel happens in hours, days or weeks. If you're walking for 14 hours of the day, stopping in the middle to fight a couple bears, then take a moment to rest your legs and eat something, an hour makes sense. If you're running around like a superhero and each "encounter" is immediately followed by another on the next page, a short rest might be a minute. You also have to note that in the normal D&D tradition, rests aren't guaranteed - it's relatively common to have a resting party interrupted by the area they are in.

In the average dungeon crawler, the party is in a non-static environment. The monsters are already in the dungeon, not procedurally generated as they approach; the dungeon denizens are also active living (or at least animate) creatures that aren't frozen in place until the door opens. So if you take out a group of, say, unusually deadly goblins in the first room, then take an hour to bandage your leg and make a sandwich, there's a non-zero chance that nothing will happen. There's also a chance that, within that hour, the other goblins that went to the Gobsco, the goblin market, will return to see a bunch of hygiene-deficient adventurers eating a sandwich next to the deceased bodies of their in-laws... at which point the rest is interrupted as the party is attacked again. At the same time, they could be attack immediately after that 1 hour is complete, so just as the party is about to advance deeper.

And that's just one way to frame it. The sounds of one encounter might draw attention by another party which is slowly, carefully trying to see what the commotion was. Unless you're scoping out a castle or bank, it might be an hour or three between patrols in this part of the woods. There are passers-by, people who were outgoing that are now returning, and groups that might have been following the party to begin with and just needed that hour to catch up. If the party is wandering through an actual underground dungeon, they can likely find a small area where they can brace the door and hang out for an hour to have that short rest - the denizens of the dungeon will almost certainly find them in 8 hours, but significantly less likely in just the next hour.

I'm a big fan of the short rest analog in Pathfinder 2e. Instead of having a specific named "short rest" mechanic, most of the exploration actions take about 10 minutes. Treating wounds, refocusing spells, identifying magic or alchemy, repairing your shields - it's in 10 minute increments. The Stamina Variant, which I have my group using, breaks hit points into health and stamina, and includes a "Take a breather" action, which restores 100% of their stamina in 10 minutes - however, they can only do that a couple of times a day, and Stamina (which grows faster than their health) isn't impacted by healing magic.

In 5e, the low-key design reason for short rests is that the true health resource isn't hit points, but hit dice. Damage to the players and hit point reduction is just there to create short rests - short rests drain the players of their hit dice, which only refresh half on a long rest. If you want to properly challenge your party, regardless of your encounter loop, you need to be dealing them enough damage AND giving them the short rests to burn their hit dice.

If a Short rest doesn't work for your style of encounter loop, change it. Maybe you're using the healing surge variant in the DMG, maybe your short rests are 10 minutes rather than an hour. If your normal encounter loop is a massive battle - Helm's Deep or Minas Tirith level fights - maybe there is a single minute between the party attacking a single squad, and then attacking the next squad.

The Cypher System has an interesting way of doing this sort of healing - your recovery rolls are all the same, but grow in how long it takes to perform. The first is a single action; the second is 10 minutes. Then an hour, then 10 hours. I haven't tried it myself, as I was introduced to the system right when my group transitioned from 5e to PF2e, but if you add that type of scaling for the short rests - one action, 10 minutes, 1 hour - I think that would work.