New theory: Super Mario Galaxy is the bridge between the main games and the sports games. (stop reading if you haven't finished SMG)
When the universe was recreated at the end, it basically became the
theme park version of the universe as seen in the main games (SMB, SM64, SMRPG, etc.). Characters and locations were recreated that really shouldn't be coexisting, like Mario and Baby Mario, or Luigi's old mansion and Luigi's new mansion, the new Bowser was just a rude party-crasher, and the Koopalings may have gotten left out of it all.
Currently, I'm only applying this once, and the only games that I'm putting in the new alternate universe are the Sports, Kart, and possibly Party games (see below). I don't think it needs to be used to separate the 2D games, the 3D games, the M&L series, the PM series, and everything else into its own universe (or even every game, as some have suggested); but as a single, one-time event, it's the tidiest explanation I can think of for how Mario and Bowser went from mortal enemies to sharing a kart.
The Mario Party games are usually said to take place in Mario Party Land. This could be the name of the new universe, or it could be another parallel universe entirely.