Not quite sure of the logic there. Or what double declutching has to do with it either tbh! The sequence is approach corner, brake, change down to correct gear with blip of throttle to match revs and avoid unsettling the rear (i.e. heel and toe), turn in, feather throttle to maintain weight balance of car and desired line, feed in throttle and exit corner. Possibly with braking, and turn in overlapped slightly (trail braking) to reduce understeer if necessary. There's no doubt that can be done far better in a manual which will mean better cornering speed and exit out of corners. But you can also screw it up in a manual by getting the wrong gear or not being smooth enough and unsettling the rear.
Also, all manuals have the LSD, whereas most autos don't. That makes a big difference to the way the car drives.
But hey, nobody drives on a track all the time anyway! Personally I think it's a far more involving drive in a manual, I bought a Supra because I love driving and it's an event every time I go anywhere. I drive it every day to work and I'd hate an auto, if I wanted to sit there doing nothing I would have bought a different car. But it's a personal opinion thing.