While others have given excellent answers regarding visual clarity, art resources, and gameplay complexity, I'll add that a major reason is that I haven't seen explicitly stated, though it has perhaps been assumed, is that the Beat 'em Up genre includes side-scrolling as part of its definition.
Doing a Beat 'em Up in 3D has another name. Either they're a "Spectacle Fighter" or a "Hack and Slash" game or possibly the extremely non-specific "Action" label gets involved.
But really, what are the essential parts of being a Beat 'em Up? While I'm not aware of a formal definition, I'd suggest that if the side-scrolling gameplay isn't part of the definition we typically have the following attributes:
- The game is primarily based on fighting enemies in real time by controlling a single character.
- The presence of enemies typically prevents the player from moving forward. Classically the screen mysteriously stops scrolling, but there could be locking doors or some other mechanism.
- Usually multiple enemies will appear at a time.
- Sometimes defeating a wave of enemies will cause even more to appear before the player can leave.
- Progression is mostly linear.
- The player most likely has at least a few different attacks, probably including a ground combo that's performed by repeatedly hitting the same attack button, and a jumping attack.
Of course, genre definitions are a difficult thing and even classic Beat 'em Ups aren't perfectly rigid on these. To take examples from Battletoads: Turbo Tunnel, Clinger Wingers, and that part where you jump on snakes all are very different from typical Beat 'em Up gameplay.
Keeping all this in mind, you could see Devil May Cry, Bayonetta, Darksiders, and God of War games as Beat 'em Ups on at least some level. There are lots of examples of "Beat 'em Up-ish" games that don't include retro Beat 'em Up conventions, but then they don't look like retro Beat 'em Ups.