Executive pay is supply and demand. The mayor is being paid $450k because a person with the necessary skills was willing to take that salary (after fighting off opponents) to become mayor. Mayor comes with prestige, so more people want to be mayor, and $450k is not a terrible incentive to go after. If the government paid $80k a year, no one would become mayor. If they paid $1m a year, too many qualified people might be interested, or – the right people might become interested.
Imagine you’re a CEO who successfully ran and sold a business for $250m. You now have at least $25m. Why would you ever want to work an intense job again? Being CEO is exhausting.
Executives are paid a lot of money because they’ve already made a lot of money: if you want to incentivize them there has to actually be something at stake.
That said, these decisions are usually made by a board, which is small and has limited knowledge.
There is plenty of room for them to miscalibrate, too, but paying too much for an executive is bad business. Paying too little is, too.