But that guardians doesn't even have to do anything he can just send someone else to do it because he's the king/dictator

The big difference here being the only people new monarchy would want is the vanguard, People who have yet to show any sign of selfish behavior, people who were put there for a reason to begin with, they're trustworthy hard working individuals who again are selfless, they only care for the good of the city and the people below, to protect and to help in anyway. The only person who people seem to distrust in the game and lore is the speaker and xur i guess. New monarchy isn't going around asking every guardian to be their leader, they're looking for certain qualities and if they see a flaw will pass on a person in the blink of an eye. The vanguard members all being interest and I believe at one point the crucible guy was an interest at one point but they gave up on him after seeing his general attitude. If you've read and listened to NPC conversations the new monarchy aren't idiots they wouldn't allow someone with a lot of flaws and shady behavior lead anyone.

U bring up they have a good recruitment process but I'll stick with fwc

Ayy, I can dig that, my warlocks about to go there. I'm not here to recruit people for some vidya clan, I'm just saying they aren't bad though I don't fully agree with just a single leader, I'd actually enjoy seeing them boot the speaker and just give power to the 3 vanguard members.