Nah. Short rests as they are in 5e are awful. There are very few situations where a party can take a short rest but not a long rest, so you generally only get to use short rest abilities once per day anyway, two if you're really lucky. But if they're only 5-10 minutes long, they become per-encounter abilities, and that's a lot more fun. I mean, I think a warlock who could cast two fireballs per encounter would be pretty neat.I generally agree with your thoughts on psionics. They idea of making a short rest 5 minutes and tying Warlock spells to that would be even more awful than the current Warlock.
In 4e, powers were either at-will, per-encounter (meaning you recovered them on a 5-minute short rest), or daily. This created a clear delineation between what sort of power levels were appropriate for the different abilities. But with a 1-hour short rest, they become resources you may or may not be able to use again that day, and that's weird.