Chances are they engage with much less and obviously don't have interactions with thousands of people and are keeping all of that straight in their head, so this is not a good reason.
You don't get credit because you oversaw a public worker whom you've never engaged with.
>makes decisions that influence hundreds of millions of dollars of spending
They also have access to (sometimes) smart people to filter through information and distill it down for them which is honestly the hardest part, not the decision making. It is unlikely they are compensated compared to the work they put in.
I'm not saying the job is easy, but they aren't doing it all themselves and the core problem is that the people underneath them are probably making no where near $450k. Salary just doesn't correlate to actual effort these days.
That said, $450k for a mayor is fine. Someone who can become a mayor can easily be a corporate executive making millions.