Jockstraps are designed to hold up and secure the penis and especially the testicles. Jockstraps have nothing to do with the butt.
However, some kinds of underwear now have jockstrap-like functions in front but coverage in back.
If there was fabric in the back, it would bunch up and make you sweat. The leg straps keep the front pouch as tight as possible, tighter than briefs would be, giving you better support for working out.
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Jockstraps have less material, to keep everything cooler and allow more freedom of movement. They also tend to fit more tightly to offer better support.