True, but Musk is an exception. And deliberately so, his media image was one of the things that made Tesla so notable. But we’re seeing recently that it goes both ways.
Musk was the PR, press and Marketing departments rolled into one for Tesla and X, so much so that he fired the PR team at Twitter.
"The public doesn't care who the CEO is" is certifiably not true for Musk ventures, and Musk exploited that brand value in the past positively. The inauguration Seig Heil, and the subsequent DOGE misadventures are the other side of that "personal brand" coin, which very much exists for this CEO.