Why wouldn't everyone be S rank? In One Punch Man, the Rank 1s of each lettered-rank have the opportunity to move up to the next rank.

After that, everyone in that lettered-rank moves up a rank.

Why wouldn't everyone keep moving up until they're all S-rank?
As you stated, you must be rank 1 to receive a promotion. The current rank 1 in A-Class is the hero Sweet Mask. Sweet mask made a point that the reason he stays rank 1 in A-Class instead of moving up to S-Class is to prevent unworthy heroes from being promoted.  



Aside from being rank 1, you must also pass an interview. Ultimately, the decision to move up is not in the hero's hands but is the association's decision. Saitama had already decided that he wanted to move up, but there was still much consultation and discussion of whether or not he should be allowed to move up before he was given the promotion. 

From the One-Punch Man Wikia:


  Overhead of the interview, there are several Heroes Association staff observing and discussing about Saitama. They discuss whether or not he is a sham. After a short discussion, Sweet Mask is seen as an advisor on whether or not Saitama should move up. Sweet Mask replies that they do not need him for such as trivial task as promoting someone to B-Class. Sweet Mask additionally states that he only wants a say in promoting people to Class A and higher as they tend to have a strong influence on the association's image. 


The fact that Sweet Mask was consulted here instead of the association just promoting Saitama as soon as he asked to be promoted shows there is more to the promotions than just reaching rank 1.