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In Gamma World 7e, are PC powers only used once per encounter?
If so, how about monster powers, are they only used once per encounter?
I know it states "you renew your encounter powers" during a "rest".
Unlike D&D where you have to "rest" to remember your spells, the PC powers in GW are who the character is built on with their origins, so why the limit on using a natural power?
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.
Gamma World has both Encounter and At-Will Powers
Player characters and Monsters in Gamma World have both Encounter and At-Will powers. Their name indicates the frequency with which they may be used. At-will powers may be used, 'at-will,' or multiple times within a given encounter. Encounter powers may only be used once per encounter.
For the purpose of story, I tend to view those powers as actions or abilities that take a physical or mental toll on the individual carrying them out. This makes a great deal of sense as many of the Encounter abilities are related to extreme actions granted to you by your mutations, rather than their more subdued at-will counterparts. As SevenSidedDie stated in his answer, this gives some powers a more cinematic appeal.
Mechanically, this breakdown gives you an array of powers that have different impacts during a combat encounter, and provide additional opportunities for tactics/strategy as PCs and the GM budget out their power uses.
