Because the standard theory is only a smidgen true. The real reason is that with both parties on the same page on segregation, the issue was off the table. So the next 20-30 years were spent trying to woo southern voters on other issues, like crime, education, welfare, abortion, prayer in schools, guns, flag burning…
and actually, Bill Clinton won a lot of southern states. The period of the South being dominant for the GOP at the Presidential level lasted all of one election: 2004. Democrats were still able to be competitive by running candidates who had southern views on the issues.