Mixing in a gym can be done effectively, but... you have to acoustically treat it somehow. We have walls that are physically hard fiberglass panels (non-reflective acoustically, and yet don't dent from a basketball hit), we hang huge, heavy floor to ceiling drapes (which also make a nice fan shaped layout), and the stage we drag out every week (oh, my aching back) is carpeted, which helps slow down things a little as well. Yes, it takes a lot of time each week to do this transformation, but it works.
The odd thing about the gym is that it's acoustically treated enough that basketball games soud "unnatural" - with 3 games going in the gym at the same time, you can actually tell which court a whistle is blown on.
Once the room is half decent, then you can think about loudpeakers with tighter coverage, etc., - if you leave it live, don't expect the gear to make up the difference. Acoustical problems are best treated with acoustical solutions. You don't fix bad brakes on your car by working on the engine; don't expect better speakers to fix your acoustics.
And yes, don't fly speakers if you don't know what you're doing. The life you save may be your own.