I'm not convinced that Brooks is a good coach. He couldn't really put together a cogent team in OKC, and hasn't done much in Washington either. I wouldn't put him in "coaches I would immediately fire" camp (Joe Prunty), but I wouldn't put him in the top half of the coaches in the league either. A small part of me thinks he ended up in Washington to lure Durant.
He definitely isn't the right coach for the hilarious egos in Washington. I love the way John Wall plays, but I'm honestly convinced that the locker room they have is at least partly on his shoulders. He is a prickly dude, and doesn't come off to me like a guy who would foster a good locker room. Maybe I just have him and Cousins linked in my brain from their Kentucky days, but both of them seem to have a heavy amount of sour to their demeanor. It feels like Washington just has too many of those guys. I don't think I've ever seen any of them having fun while playing, even when they're winning.
Beal is a good player, and seems like a nice guy but he has to be your 3rd best guy. I also think the return on Beal wouldn't be quote as good. He's 3 years younger than Wall and is way easier to fit in team building, so I'd probably try to build around him, Oubre and Porter.
If it were me, I'd move Wall. I think they can get a good return on an allstar PG signed for a bunch of years in the prime of his career. Probably 1 lightly protected first rounders and at least 1 young prospect. Something like Lonzo + a top-3 protected pick next year. That is the kind of return they should expect.
A Leonard/Wall trade would be interesting and WAS would have to throw in Oubre, but I'm not sure I'd do that if I were the Spurs. I think you have to rebuild if you trade Kawhi, and I don't think John Wall is the guy you rebuild around.