A couple of thoughts on this:
1) I have no dog in this hunt, so in the end, I'm not terribly concerned about the consequences. I live an hour from Milwaukee in NE Illinois and we have enough of our own problems, thank you very much. Our state spent somewhere between $200 million and $400 million more than it needed to on a publicly financed football stadium to preserve a crumbling war memorial and to build a toilet seat inside some Greek columns -- so who are we to judge!
2) The only way I could imagine that a privately financed stadium works is if the Bradley Center and the old Milwaukee Arena are torn down. I don't see that as necessarily an automatic in this debate. The Arena, which has not hosted the Bucks or Marquette since 1986, is still standing and I wonder whether the Convention Center District would be open to removing the Arena-Auditorium for an asset they did not control or potentially benefit from. Both sites have to go to ensure the new facility has no competition.
3) The model for a privately financed stadium is Dodger Stadium in Los Angeles. The City of Los Angeles condemned the land in Chavez Ravine for the stadium and improvements. Walter O'Malley, the then-owner of the Dodgers, financed the stadium's construction and operated it. One of the big contributors to the eventual success of the Dodgers was Union Oil Company of California's sponsorship, which repaid a financial commitment that company made to the Dodgers. Union Oil sponsored Dodger broadcasts and was the only advertising in Dodger Stadium for years.
4) For a privately financed stadium to work, the owners would require a significant commitment from Marquette regarding use of the stadium and, probably, a commitment from the Admirals and the UWM Panthers as well. I also think the number of concerts would have to rise exponentially. I'm no expert in stadium economics, but I suspect that only Marquette and the concerts could benefit from the incremental amenities and capacity with the new arena.
5) I don't know what to think of the possibility of losing the Bucks. I do know that when the Milwaukee Braves left town in 1965 for Atlanta, it left a huge hole in the hearts of baseball fans in Southeast Wisconsin. The ugliness surrounding the Braves' move south, the bitterness both before and after the team left, really didn't subside until a good part of the generation that was huge Braves fans basically died. The Brewers did a lot to fill the hole, but the lingering animosity toward major league baseball lasted for a long time. I suspect the Bucks have been so bad for so long that the animosity won't be as severe but who knows? Unlike major league baseball, if the Bucks leave, the NBA is NEVER coming back.
There is no doubt in my mind that a private stadium CAN be financed by almost any owner in the NBA. The problem is, they just don't want to, and to this point, most don't have to.
Cities will finance and build arenas and stadiums and give the teams all of the, parking, concessions, etc.
Why would any owner pay for it themselves when there are markets out there that will pay for them? It's happened across all pro sports.
Why would the Wilf's pay for a new Vikings Stadium when they can get the State of MN to do it for them? Way less risk, way less $ up front, and they still get to reap all of the benefits.
The Bucks ownership isn't going to build without public funds. Won't happen. They will want a good amount of public $. That's how it works.