Really? You expect the CEO to make all significant decisions, all on his own? No wonder you think the CEO of a billion-dollar company needs a 7-digit salary.
I think the main job of CEO is to appoint useful directors, and promote competent managers. That's certainly a challenging job; but it's a job you can learn, like any management job. I'd even agree that most people are unsuited to that work, as most people are unsuited to any kind of management.
But it doesn't call for some kind of superstar, a one-off snowflake "talent".
> But our mayor oversees thousands of employees and makes decisions that influence hundreds of millions of dollars of spending.
Right; arguably your Mayor might be worth $450K. I'd be upset about my representative being paid that much out of scarce public funds; but that's not even in the same ballpark as the going rate for the CEO of a billion-dollar company.