The modern CEO job is completely broken

The difficulty here is at any not tiny company nobody except a select few people at the very top can actually be led by the CEO in the way you are describing, and if they tried to lead the masses so to speak, it usually turns into a cult of personality, which actually doesn't look great to investors. So it's very difficult to lead large organizations in a way that doesn't necessarily result in scheming behind closed doors with a small club of in people, which doesn't look great either.

It seems to be almost a requirement for the CEO to be disliked for those reasons.

Obviously AI wouldn't be better and would be a black box to most employees, just like CEOs are already.