In A Study in Pink, Donovan even says Sherlock  "gets off on" his work...and then he asks John along and John says "Oh, God, yes!" So the invitation to solve crimes becomes something of a seduction.

Not to mention when he's trying to reunite with John in TEH, and tries to "tempt" John with the thought of, "the thrill of the chase, the blood pumping through your veins, just the two of us." If you think about, that last part, "just the two of us," doesn't really belong there, or doesn't HAVE to be there. Sherlock could have said, "you're thrilled by the thrill of the chase"; but here, he's essentially saying John is thrilled when it's just him and Sherlock.

While I see the argument for the friendship Sherlock finds in "solving crimes together,"  I believe that was not Sherlock's original motivation for involving John and later giving Molly a try.  At the very beginning, in ASIP, Sherlock asks Lestrade who's on the case, and then says, "Anderson won't work with me."  Lestrade responds, "Well, he won't be your assistant."  And Sherlock says, "I NEED and assistant!"

This tells me Sherlock's original motivation for inviting John onto the case was to try him out as an assistant; you could almost see the wheels turning: A doctor? Used to violence? Hmmm...   Plus, as he points out in the same episode, he thinks better when he talks aloud, and the skull just attracts attention. He got more than he bargained for with John of course; he got a partner and a friend

Likewise with Molly and later more-or-less jokingly with Janine, he was looking for an assistant.  And it may be that his later efforts to replace John stemmed from a need for not only and assistant but also a friend. 

Who knows what goes on in that funny little brain of his?