If you went back to playing in the actual regions like they used to, you could reseed each round. So there wouldn't be any travel issues. You can have 1/16, 4/13, 5/12, 8/9 all in one site and 2/15, 3/14, 6/11, 7/10 all in another. IMO that would be a better way to determine a champ. I hate that FAU could make a S16 by beating an 8 and a 16 seed. Or that San Diego State can by beating a 12 and a 13 seed. Or that Missouri can by beating a 10 and a 15 seed. That is more luck of the draw.
So we would have...
East
Tennessee vs FDU
Duke vs FAU
Marquette vs Michigan State (same)
Kansas State vs Kentucky (same)
South
Alabama vs Furman
San Diego State vs Maryland
Baylor vs Princeton
Creighton vs Missouri
Midwest
Houston vs Auburn (same)
Indiana vs Miami (same)
Texas vs Pitt
Xavier vs Penn State
West
Kansas vs Arkansas (same)
UConn vs Saint Mary's (same)
UCLA vs Northwestern (same)
Gonzaga vs TCU (same)
For the S16 you stay in your region but those teams are reseeded. Same for the F4 getting reseeded.
The great thing is you can still for the most part keep the brackets. Since most people fill it out digitally it is pretty easy to have the matchups auto fill.
Let's say you picked Purdue, Memphis, Tennessee, Oral Roberts, Providence, Kansas State, USC, Marquette in your bracket. Then the next round in your bracket it would be Purdue vs Oral Roberts, Tennessee vs Memphis, Marquette vs Providence, Kansas State vs USC. Next you have Purdue vs Providence and Kansas State vs Tennessee. And finally Purdue vs Tennessee, with Tennessee in the F4. So you would be 3-5 in that 1st round, still have two S16 teams left, one E8, and one F4.