First thing, gotta point out a factual inaccuracy in your post. There is no suspension simply for fighting in hockey, just the mandatory 5 minute major penalty. Leaving the bench to get into a fight, on the other hand, is an automatic 10 game suspension in the NHL. The reason for that being that bench clearing brawls used to be so common that the only way to put an end to it was a swift, harsh punishment.
Fighting isn't technically "allowed" in baseball. Benches clear without any real fight taking place and that kind of thing generally goes unpunished. Throwing punches or any other kind of physical altercation will get you suspended as well it should.
My problem is that hitters today are far too sensitive. If they get plunked on the foot with an 0-2 curveball, they're staring out at the mound and jawing at the pitcher. Pitchers have basically had the inside corner of the plate taken away from them by hyper-sensitive hitters who treat every inside pitch as if it's an insult to their family and umpires who pander to them by issuing warnings for no real reason. A lot of these bench clearing incidents start because of this and would be prevented if hitters would stop acting like babies every time a pitch comes in on them.
I know I trailed off the subject a bit there, but that's something that's been bothering me for quite some time.