I always chuckle when I see on IG that Anthony has been in L.A. for weeks at a time lol.
Hedi already did that when at YSL, also at Celine.
Nicolas does it too, he has owned several houses there already, and his bf is from LA.
Anthony rents but spends a lot of time there for Saint-Laurent Productions, you could say he is not very interested in fashion anymore.
But both Nicolas and Anthony have teams and assistants in LA and Paris, I don't know if Hedi has more than his former photographing team here now.
It's not really a very big disturbance because Pinault lives in LA part-time, and for Nicolas, the Arnaults all have very extensive real estate. They are literally playing Monopoly in Beverly Hills right now, Bernard Arnault even drives himself in his own car (while being paranoid in France), and they own private Airbus A350s (not the company planes) to jump between LA and Paris.
As for Karl, I have seen him designing several collections for various houses (Chanel, Chloé, Fendi) in a couple of hours, all the very same day, then just send couriers to the studios and calling to explain the sketches, giving instructions for the fabrics and colourways. I have seen him faxing entirely collections too. Then I assume he would go in the studio when the "toiles" are ready and for choosing the fabrics. That's where and when good
premières and assistants like Virginie Viard are needed but that does not give them any distinctive visions or talent by association.
Yves also always designed at home, Deauville, Paris or Marrakech, he went to the studio to choose fabrics with Anne-Marie Munoz and Loulou de la Falaise, design the smaller elements, and finish the cut and tailoring.