That's not any function of the fictional time taken, though. You are deciding to change the frequency of rest interruptions and reducing the number of game-functional "time ticks" the players have to complete the quest; you could do all that with any imagined "duration" for the short rests and concoct a plausible (and acceptable, to some groups) justification for doing so.
I think that you are jumbling up things that are purely a matter of depiction and imagined fictional event with things that are changes to the system. If the descriptive elements are all changed to suit, then the imagined scales of time and distance can be arbitrarily set.
I'm pretty sure that our base assumptions here vary, probably due to playstyle differences. What you're saying makes me think of the time Varsuvius explained how often encounters are checked for (in OotS): once along the way. It sounds like you probably fall closer to that approach than I do- for me, the frequency of encounter checks depends strictly upon the world. There might be more or less depending on the pcs' mode of travel, but if they ride horses for forty days, there might be several sessions of random encounters before they reach their destination. I don't arbitrarily change the world to suit the pcs; I feel very strongly about the milieu standing on its own two feet and treat the campaign very much in the fashion that Gygax wrote about, as a setting with many independent pcs adventuring in it. Heck, I even run different systems in the same setting- I run both a 1e and a 4e group (with a lot of overlap) set in my world.
So, yes, you
could arbitrarily set the scales, but I don't- I set them according to in-world logic. Therefore, the length of a short rest has a dramatic effect on play in my campaign.
To take a simple example, if the imagined duration of a short rest is 5 minutes and a goblin patrol move 100' per minute, then goblins 500' away will take a short rest to reach us. Exactly the same is true if the short rest duration is imagined to be an hour, the goblins move 1 mile per hour and the goblins are 5 miles away. You compose the rules by deciding how frequent you want the interruptions, how many "time ticks" you want the players to have to finish quests and so on and then either set the size and "dilution" of the world or set the rest "duration" to suit.
The risk if you do otherwise is that the activities you intend your game to be about will prove to be practically impossible for the characters to engage in.
Again, it's a matter of playstyle. I intend my game to be 'about' the pcs interacting with the world. I'm a very sandbox-style dm, with very little "story" that doesn't come about because of pcs interacting with npcs and so on. I don't mind if the pcs get sidetracked, abandon adventures, leave sites half-explored, etc. In fact, one of the best game sessions I've ever run was for a halfling party, and almost the whole session involved going back and forth around a crossroads and eating giant eagle eggs. Surely, that's not a traditional adventure- and to some groups, it might sound absolutely lame. And that's fine. There are plenty of adventures I hear about that sound absolutely lame to me (usually if they involve any level of forcing pcs into specific decisions). It's all a matter of playstyle. As long as my group is having fun, I'm satisfied, and I achieve a good game specifically through campaign integrity. The 4e group, if they're in location A, will find the same stuff, will check encounters with the same frequency, as the 1e group in the same location. Yes, to one group a monster might be a level 1 minion skirmisher and to the other the same monster might simply be a 1/2 HD monster- because the systems are different, the stats will change- but the
world is the same.