It doesn't have to be but like I said earlier if you have a home, shouldn't you play there?
Using the same central location for Olympic sport championships makes it easier for everyone. You don't need to scout locations, find accommodations, practice fields, etc. Schools won't have to travel to Miami one year, New York another, Atlanta the next, etc.
If schools aren't going to travel there, is there even a need for a nearby airport?
Tampa might not be a bad idea either. Not hard to get to. Weather for championships will be good. Although it might be too hot for Lax. Who wouldn't want to go to an ACCT with nice weather outside in early March? Or an ACCG in early December? It is relatively neutral. FSU would have an advantage in football. No other conference has a claim like the SEC does with ATL.
I don't like that the ACCT is always changing locations. It would be nice to have a permanent home as long as it isn't Greensboro.