it was still a logistical bottleneck, however long it was open for
And trying to supply the entire invasion force through southern france wouldnt have been a massive bottleneck of staggering proportions?
As it was they suffered major problems with fuel supplies, stiffer resistance (which it likely would have been without Nazis forces being moved north to counter the invasion there) would only have made that problem worse.
There is also no certainty that the Nazis wouldnt destroy the ports this time around. While they didnt in OTL, this time it would be clear that the invasion is the real deal, whereas in OTL the allies were already ashore and rampaging through France. The priority could easily have been to do as much damage as possible rather than bugging out before being cut off.
So the destruction of a few southern ports was a much lower priority than it would here. And without those ports the invasion would be doomed to fail. At least with Normandy they had the mulberrys to use instead, I dont know if it would be at all possible to have the same in southern france!
No, far better to go into Normandy first, it maximises all your advantages and minimises the risks as much as possible, a direct attempt into southern france first completely flips that around.
Once the main invasion is successful, then you can use the valuable experience you have gained launching this kind of amphibious operation and do it again elsewhere as the overal strategic situation has radically changed in your favour.