Why did they avoid sex?

It's hard to say and I think it's best left in a shroud of uncertainty, perhaps this was intentional. Paul's feelings were certainly complicated, because he saw this woman as "pure", "unadulterated", and he really liked her. Having sex with her would have relegated her to the same category as his previous conquests, and I suppose he felt uneasy about that because she was special to him. Sure, he was attracted to Noel, but he finally found someone who didn't ignite a purely lust driven response and he wanted to treat it differently. This is where the title comes in, I believe, because "all the real girls" indicated Noel, who taught Paul that it's possible to experience desire and love, something he had previously as mutually exclusive, even if it was unintentional on her behalf.