Compression clothing is useful for moving more weight.
An example is the powerlifter a good bench shirt can add a lot of weight to his bench press. Briefs can add weight to his squat, a full squat suit - even more.
It's just an extreme example of safety equipment carried to extremes. Because of my bad CNS, my legs are unreliable. Sometimes they don't want to work right so I'll wrap my knees to be able to squat. I may wrap them today and do 140lbs, next time I won't wrap them and do 160lbs (I'm small and weak and doing the 10's). Used properly compression gear is safety equipment. Otherwise they are a crutch to allow you to use more weight than your body is able to handle - leading to injuries eventually.
Another example of how they are useful. I swim/bike/run in just a pair of swim trunks and a tee shirt. When I compete in a triathlon, I use a wetsuit that compresses my legs - better kicking power with extra floatation. I wear tri briefs which are like bike shorts with less padding to compress my thighs, this increases my peddling power on the bike and keeps me from being as fatigued when I run. Sadly, kind of like in powerlifting - if all other things are equal - conditioning, strength...they guy with the best equipment will win.
Me, my sad half crippled legs, my $800.00 bike, $300.00 wetsuit, and $40.00 briefs cannot compete effectively with the other guy who is riding a $5000.00 bike, wearing a $1000.00 wetsuit, and wearing the $200.00 briefs. But I can keep up because my training is pretty much raw except when I use equpment for safety.
So to sum it up, unless there is a safety issue or you are in competition where it's needed to be on an even footing, the compression clothing is more of a hinderance than a help - train your muscles, not your gear.