> Is there any reason why someone who is more interested than me in becoming a head of state may think otherwise?
Corruption is the obvious one. Keep in mind that running for elections has a cost, people that pay for it are more likely to expect to gain something in return.
There is also the non-obvious but still existent problem of the Law simply getting in the way, so decision makers try to act outside of it.
If you defeat corruption you have more legitimacy, which helps you ask people to make sacrifices. More legitimacy also means you don't have to "spend" as much to be elected, particularly in the sense of patronage.
Perhaps, but the pessimist in me suspects that this natural legitimacy, which we all wish our politicians would have, is not near as effective as advertisements. Somehow, we have to come to terms with just how good advertisements are at affecting our decisions.
China's concept of legitimacy is "output legitimacy", which actually works pretty well. (Look at the old Shakespeare plays where disaster follows after the king is usurped)
"Advertising" can get you to the place where the U.S. is well where you can get 49% of the population who have 51% of the influence to think one party is legitimate (e.g. they take money from the koch brothers, kiss the ring of every republican donor, promise not to raise taxes; the left wing version is "green new deal", "tear up men accused of sexual harassment", ...) and not care what the other people think.
As far as I know the entire establishment turns against anyone that tries to defeat corruption (with different strength depending on what place we are talking about). That usually leads to lower legitimacy, not higher.
Corruption is the obvious one. Keep in mind that running for elections has a cost, people that pay for it are more likely to expect to gain something in return.
There is also the non-obvious but still existent problem of the Law simply getting in the way, so decision makers try to act outside of it.