Since I am never disappointed with the breadth and depth of this board's collective knowledge.....
How does it work from a scheduling standpoint for all of the NBA/NHL etc. teams who play in arenas that also host conference tournaments and NCAA tournament games? Obviously they can schedule a string of road games for many teams but at some point won't there will be an imbalance if too many venues are hosting?
Conference tournaments are contracted and scheduled/booked years out, typically, so they'd be on the books long before the pro leagues set their schedules, thus I presume the leagues just work around the dates available in venues. Conference tournaments don't really use that much time - maybe 5-6 days or so, which is really only a couple games.
There are 32 D-I conferences, of which only 8 are held at pro facilities (5 NBA, 2 NHL, and 1 with tenants from both leagues), and 1 of these is held a week before all the others (MVC).
In actuality, the first and second rounds of the NCAA tournament, disrupting 3 venues of each league this year, is a bigger problem for the NHL than conference tournaments -- but still negligible.