The studio did approach Miyazaki's son Goro Miyazaki many times to become a successor to run the studio, but the younger Miyazaki has so far refused all offers, and Hayao Miyazaki also opposes his son becoming the studio's head.

Man, Goro's relationship with his father is an interesting story on it's own. For most part of your childhood your father is barely there, mostly producing movies for other children and when you're grown up you try to catch up to your father in his industry and he thinks that you're fucking worthless.

whenever i hear the word 'aquired' i automatically assume the worst

Chihiro 2: Spirited Again

Could be worse, like it being assimilated into Disney and spread profit-maximisingly thin like Marvel/Star Wars, or Time Warner so that Zaslav can torch the archives out of sheer spite.

I'm willing to believe somehow this is Miyazaki's son's fault

Does he actually think he's worthless? I can imagine various other reasons for him not wanting his son to take over. Being unfitting or not good enough doesn't make him worthless for example.

Ghibli is done anyway with Miyazaki resigning. I assume that moving forward, ghibli will foremost be an IP holder making money off of licensing.