With the standard that we've seen the studio release over the years I don't think it's any worry. They wouldn't let an amateur direct, so young Master Miyazaki must have some skill, despite the implications being son of a great director would bring.
I have to say I think "father" Miyazaki's appeal doesn't so much spring from his skill as a director, more in his ability to capture obscure and often overlooked idiosyncrasies that exist within the human character, born out of his experience in life. When I've seen clips of him with his animation team, he focused things like the animal movement on things he'd seen, like snakes falling from tree's etc. and the way Chiro's parents eat on people he knew etc. It's all on the Spirted Away special Features - Anyway, what I'm getting at, in a round-about-kind-of-way, is that as long as people don't judge young Miyazaki's directing talnet by his father's mature and experienced standards, it should be fine.