The only problem would be years where a school like Union gets a #1 seed. Or a similar type infrastructure. That goes back to what I posted earlier in the thread. You would need to know ahead of times what schools are capable of hosting and those schools would need to be on board with keeping the arena available for that weekend. But I did mention baseball. The format would be very similar. Of course, you could also alleviate some of this by having the round of 16 be all on campus between only two teams each. So 1-16, 2-15 etc. Then any school could "host" and it gets you down to 8 teams after that.
The "Union problem" is a red herring. Not every facility is an NHL arena. Just like not every college baseball facility is Yankee stadium.
For teams like Mankato who play at a site they do not control, those teams already have to make plans for
possible, but not guaranteed games as part of their conference playoffs.
The baseball system works really well. You identify the host seeds for the Super-regionals (which are really just the equivalent of hockey's tournament). If the host seed loses at the regional level, or if for some other reason the host seed can't host, then the remaining teams get to "bid" on hosting. Usually the program with the best facility wins that bid, but it wouldn't have to be that way. You could give the #2 seed a chance to host, and so on.
I also think the host can choose to host it at a neutral site. In fact, I think one of the baseball Super Regionals got moved to a neutral site by the host last year due to pandemic restrictions.
As for the question as to whether there are multiple cities capable of hosting the FF, sure. But I will tell you this. I attended every WCHA conference tournament in St. Paul from its inception to when western college hockey blew up in 2014. I also frequently attend the College World Series in Omaha. Those two events were/are spectacular, I believe in large part due to the common experience in the common location. The host knows how to run the event. The host hotels, bars and restaurants have their plans in place.
It makes for a wonderful experience.