Why isn't this done in the USA? Good question.
I think the real reason would be local police or state gaming commissions. A lot of what goes on at a catfight or wrestling convention could be construed as solicitation or gambling by some. I know it's not, but all it takes is a few people asking questions to screw things up.
There are three ways to do an event like this, and I only think one would work.
First - rent out a large public space and invite vendors to set up and have a ring where women would do their matches. This was tried and did not work... too much up front cost... too visible
Second - get some women to fight in a tourney and charge people $20 or $50 to watch. The purse goes to the winner. The state gaming commission would want a piece of this. With an entrance price that low, you might get spectators who get too rowdy and police are involved. Heck, one person could call the police that isn't even there and break this up. Too risky. Plus, not one is traveling far for this.
Third - This is what I would do. First, I would charge at least $500 per person or couple. If you charge that much, people will travel. Plus, at that price, they are less likely to to get drunk and rowdy and screw things up.
Research an airbnb that has land and has a lot of bedrooms. Start the event on a Friday and end it Sunday evening. The only people who sleep at the airbnb are the session wresters or paid fighters and the organizer. Paying people would need to find their own accommodations. Start with a group dinner on Friday night. Make that more of a social night. No fighting. Create a match card for the next day. If people want to do privates, that can be done in the rooms of the session wresters on site or they could be done back at hotel rooms.
All food and drink are provided at the airbnb. I would say matches start after 1 p.m. on Saturday and a nice dinner would be provided. Sunday morning could have more private matches, but the airbnb would be shutting down.
So for $500 or so, you get a social night to mingle and Saturday would be a full day of action.
I know it's expensive, but this is the way I would do it right.
Oh, no cell phones at all at the venue. They would be checked at the door. The host would create a video of the matches only using people who wanted to be on video.
Atlanta would be the first place I would look at has a hosting city.