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.
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.