Charlie's desire to have the surgery stems from his desire to have friends. Consider this quote from the book:
I dont care so much about beeing famus. I just want to be smart like other pepul so I can have lots of frends who like me.
Charlie has always been isolated and alone. People may be nice to him, but no one is his friend. Even his family members do not bond with him the way they do with each other. His disability keeps him separated from other humans.
When he "gets smart," it is the same problem. He is isolated because of his genius. He is taken to a scientific convention to be shown off--like a circus act. Algernon represents the only living being that has experienced what Charlie has experienced. Algernon is also the circus act. He may not be able to understand or feel that the way Charlie does, but it makes Algernon the one creature with which Charlie does feel bonded. If he did not feel that bond, he would not have foreseen his own future.