I mean, look at it this way: everything in cricket has a plus and a minus. If you hit it, you can make runs or be caught. If you miss it, you can get byes or be bowled. If you run, you can get runs or be run out. So if you say no leg byes, then you clearly have to ban LBWs to even it out.
And to break it down further, cricket is about two things: a) the bowler getting the batsman out, and b) the batsman not getting out. Runs are a byproduct of that survival. The bat isn't really for scoring runs, it's for defending your wicket. There's no logical reason to privilege runs off the bat over runs off the body; if you're being hit on the body and aren't out LBW while legitimately trying to defend your wicket, you're surviving, and thus leg byes are a byproduct of that survival.