"I think it's worth noting these little hints that outgoing and extroverted are thought to be synonymous with "good leadership" (in the US, at least)"

I don't think it's synonymous, but it's required. To be a good leader, you need to enjoy being around and understanding people.

Most introverted people don't really enjoy either.

I've had many introverted managers and they all were horrible: lack of communication which went hand-in-hand with passive aggressive behavior.