^^^ True. So a president has to have a lot of good reason to be a president.
In the USA, the spoken theme for the whole country is FREEDOM. And a president who takes the job isn't being paid nearly enough from his regular salary. His money after retirement isn't enough, either... even with the perks, like the medical that is often turning into a sham/scam as we see with Covid.
A president loses a whole bunch of freedom just to be president. Sure, he plays golf a little. But everybody needs to relax part of the time, to make his time on the job efficiently effective.
Real politicians aren't really free. Much more fun to move to Belize or Panama, and sit out on the beach sipping... whichever you prefer.