Why Is Socrates Argue The Right To Rule In Book VI Of Republic?

After proving that the real problem is caused by democracy, Socrates suggests that people should come to philosophers for rule rather than philosophers volunteer to rule. In Book VI of Republic, Socrates provides another analogy to illustrate his point: “The natural thing is for the sick person, rich or poor, to knock at the doctor's door, and for anyone who needs to be ruled to knock at the door of the one who can rule him” (489 c). Here, in my interpretation, Socrates sardonically emphasizes that the way democratic rulers rule the city is actually ridiculous and unnatural because democratic rulers need to gain support from the public in order to rule. Oppositely, a real ruler should let citizens come him/her for help. Therefore, since democratic rulers need to gain support from the public instead of the public voluntarily come to him/her, Socrates points out that democratic rulers lack ability to rule.
In my opinion, there is nothing wrong that philosophers are extremely obsessed with truth and knowledge since that is their duty and job. Especially, in a just city, when everyone is doing their part well, philosophers actually have the ability to lead the citizens forward with their knowledge, and therefore philosophers should be the ones who rule the city. In this case, since philosophers are capable of ruling a city, they do not need to beg for others to let them rule since I do not think philosophers are really interested in ruling than seeking knowledge. Thus, it is necessary for citizens to voluntarily ask philosophers to be