One thing 4E got right was encounter powers on 5 min rest recharge.
The reason why 5 minute rests worked in 4E is that they
expected you to take one between every encounter. They
wanted you to always have your Encounter powers available for every encounter, and it didn't matter whether you took two or twenty short rests between encounters, since there was no real benefit to taking more than one.
If a short rest in 5E was 5 minutes, then it would happen between every encounter, and they'd need to adjust every short-rest power under the assumption that they would be available for every encounter forever
and that short rests would be chained if there was any benefit to doing so. You can't just say that you only benefit from two short rests per day, because that doesn't correspond to any logical in-game construct. There's no good
reason why you can't benefit from more than two short rests in a day, like how sleepiness is a logical in-game factor which prevents chaining long rests.
Given that they couldn't come up with a reason to limit characters to two short rests per day, it makes sense that a short rest would be an hour long, since that's an appropriate length where
sometimes you might have time for one (but not have time for a long rest - as you have experienced); if it was much shorter or much longer, then it would come up far
too frequently
or infrequently.