Snapedom

I quite agree that the long-term risk of the 'friends' strategy would have dissuaded Severus from taking that route. Also, I would add that it likely would come across to many as a noticeable departure from his normal behavior - a disadvantage in terms of both Severus' acting (he's definitely a method actor as far as I can see) and believability. He doesn't normally go out of his way to be on lovey-dovey terms with everyone he meets. Why would he want to risk having people start questioning the motivations of his earnest desire to be buddy-buddy with the son of his (as is well-known) deadly rival? He knows Voldie is a paranoid bastard of the 'shoot first, better safe than sorry' type. From his POV, everything points towards establishing a very conspicuous distance between them as the best way to proceed for both his own and Harry's long-term safety.

As for fanfic-type scenarios in which Severus is publicly harsh with the boy but secretly his mentor: 1) Dumbledore likely would have done (did do) all he could to nip such a relationship in the bud, and 2) given the series of misinterpretations, bad reactions, and so on that colored literally their every interaction from the get-go, there isn't really a moment where such a relationship could get started well, even if Severus had planned on it. I also wouldn't be surprised if Dumbles had been priming Severus to see the boy negatively before he even arrived, as a counter to any such plan, but that's supposition.