I would say the no limit/cash money era is when the south kinda took the reigns, ghetto dope and 400 degreez really changed the sound and aesthetic of hip hop at that point.
Nah, The South didn't really take the reigns at the time. With No Limit and CMR, it was very Louisiana focused as opposed to the whole South blowing up. That didn't happen until the early '00's. By 2005, there were movements all over The South:
Houston- Swisha House and Screwed became national
ATL- Crunk, Snap, trap, Luda, Kast reaches commercial apex
Memphis- Three Six reaches commercial apex, Young Buck
Mississippi- David Banner
Kentucky- Nappy Roots
Louisiana- CMR still viable via Big Tymers/Birdman, Lil' Wayne, and Juve gets a second wind and a huge hit with Soulja Slim
Florida- Trick Daddy became bigger. Rick Ross blew up. There was also Plies. I don't know if we're counting Pitbull and Flo-Rida
Alabama- Rich Boy
Artists from all over were hopping on Lil' Jon beats. Even some of the older heads in The South were bigger as a result. Eightball & MJG dropped one of their biggest albums in 2004. Bun B had a successful solo album. T.I. and Lil' Wayne went on to become two of the biggest rappers in Hip Hop.