Personally I think it will go down like this: Peter gets his powers and initially uses them to fight crime, but in a reckless, more self-satisfying way. Doing it more for the fun and thrill of it rather out of any sense of moral obligation. So when he finally has enough of being bullied by Flash Thompson, he doesn't hesitate to beat the crap out of him and humiliate him for revenge. Uncle Ben gets on Peter's case about it, which makes him mad. As a result, he goes out that night with an attitude of carelessness, and decides not to bother stopping the robber who runs right past him.
The more I think about it, the more I think it works. In my opinion, it hits all the same beats as the original story. It actually seems more natural and subtle, as opposed to just saying 1) He gets his powers 2) He becomes a selfish jerk 3)He learns not to be a selfish jerk and becomes a superhero.
In this case, it's about him having to grow out of his immaturity. The power and responsibility theme still applies, in fact maybe even more strongly here than in the original story.