How many of those tournaments still exist? The days of the Far West Classic are long gone. I see little to no hype for the Great Alaska Shootout anymore (only Maui seems to be a tournament of note). Bigger schools will structure these 3-games-in-3-days round robin events (4 teams) to mimic a conference tournament run, but no conference mates EVER join those (hence forget about Gonzaga or BYU as long as they're in the WCC). The chances are limted for getting a school better than the host schools.
I was in Vegas on the weekend before Christmas and caught the second day of a two-day "tournament" involving 6 schools... at MGM Grand Garden, capacity 14,000 or so. The crowd I saw would have looked small in Stott Center, and that included Boise State the day after their bowl game IN VEGAS. The two-day crowd (Oregon State played the night before), from the announced attendance and observation, MIGHT have sold out Stott. BTW, the PAC-12 put on this show.