I think that this is a good theme and I like your ideas.
A couple things I would point out.
First, I think that the Greasers are pressured by society as well. They are told that they are scum and that makes it hard for them to be anything else. The ones like Pony who want to make it have to break through the mental barriers that society has put up against them.
Second, I think the Socs are at least capable of having home problems. I think that Bob had problems at home with his parents ignoring him, right?
To me, all of this shows the idea that teens constantly feel judged by their parents and by the society they live in. And they have a hard time figuring out how to be themselves when there are all these expectations placed on them.