Yes, encounter powers can only be used once per encounter, hence the name. The rule you quote about only getting them back during a rest is literally how they work.
But why?
Because. That's really the only answer. Because that's how the game is.
If it helps, think of Gamma World 7e as running like a movie about the weird post-apocalypse instead of simulating "real" life in that world. In a movie, a big, flashy, pivotal move is only going to get used once in a certain conflict, because that's how movie screen time and plot-writing works. So too, in GW 7e, a pivotal, flashy move is only available once in a given conflict, because that's the only time it actually makes a difference in the outcome.
A note on D&D-based intuitions: In some editions of D&D, only wizards need to rest to regain their one-use powers—their spells. However, Gamma World 7e is based on D&D 4e, and in D&D 4e it's normal for a character to have powers usable at-will, once per encounter, and once per day—so that includes fighters, thieves, and the like having single-use powers too, not just spellcasters. Any intuition about how Gamma World "should" work in 7e, based on earlier editions of D&D, won't be helpful in understanding Gamma World 7e and will more likely interfere with understanding its rules.