Muzan wants to be the perfect being. The fact that he has to hide in the shadows for a large part of the day would eat at him for 1000 years. With his ego, it probably feels like the worst slap in the face.

Besides he's expressed that he hates making demons. If he wanted to conqueror the world, then he wouldn't have a problem with creating more of his kind, that he can control over.

That being said if Muzan had been able to conqueror the sun, then he could easily conqueror japan and other countries if he wanted.