Well, as far as I know, PC LAN parties have everyone bring their own setup. I guess if they can do it, so could we.
It would be a bit problematic for larger events, but considering the short length of a given match, we could run modest tourneys with only eight setups. Let's say, if eight teams were to attend, and we play round-robin style, plus finals because that's what sells tickets in the end. That would be 57 matches, each lasting about five minutes, plus, say, three minutes prep-time and handshaking. That would be 8 x 57 = 456 minutes = 7,6 hours pure game-time. Not counting prep time for the tourney itself, breaks and other time-wasters.
Yeah, ok, that's probably not very viable. We'd need at least 16 setups to cut that time down to about 4 hours. Can be done, but definitely more difficult to set up than a Smash tournament.