Status for status sake is a fact of political life

Sociometer theory suggests that people don't optimise for status directly but optimise for high self-esteem which is often correlated with high status (see That other kind of status [LW · GW]). 

I think this make sense in the context of the examples you give here.

I wonder how much this is about people in general, and how much is an effect of selection. People who do not have strong preference for status, usually do not get to the situation where they have to choose whether to be a president of a state that is losing the war. People who do not have strong preference for being #1 in the Soviet Union, usually do not become a General Secretary.

So, maybe it is more like: People who currently have high status, usually have a strong preference for high status, and will try to get more. Which would imply that to avoid having leaders who optimize for high status too much, you should select people who were not already competing for the position. (This strategy has the obvious problem that it only works as a surprise. If it becomes known, ambicious people will start optimizing for the appearance of being a person who is not competing for the position but still happens to be the right choice.)

And that is kinda a common knowledge; I don't remember the exact words now, but it goes something like "the power should not be given to those who desire it, but to those who don't".

This rings true. And most of us who realize that status is in our utility function can usually just say "Yeah but if I have higher status I'll get XYZ, so it's worth its place in my utility function, if only as a means to get XYZ."

And you've called out some situations where there is no XYZ. In those cases, would we be able to reject status for its own sake? Or is it so embedded in our utility functions that we can't help but feel driven toward it?

One possible explanatory model is that status is like money - a resource that's applicable to a huge variety of terminal goals, and something that rational agents will pursue, regardless of their actual goals. See https://www.lesswrong.com/tag/instrumental-convergence [? · GW]for a lot of related posts.

I apologize for nitpicking. But the name is Khrushchev.

>Why did Donald Trump decide to take a stressful 12-hour-a-day job in his mid seventies?

This example doesn't work particularly well for a few reasons: Firstly Trump as well as his family and friends have been able to reap tremendous financial benefits from his position (through a variety of means especially corporate capture). Secondly Trump somewhat infamously has been known to take far more vacations and do a lot less actual work than most previous presidents.