Mark, you're so right, I've done nuanced Johnny a disservice! I was thinking more of the arc that sees Baby being all geeky and posh in her cardigan and leather-jacket-Johnny initially sneering at her and being utterly dismissive, until she puts on a leotard and some makeup and learns to shake her booty and then he's all "rawrgh, c'mere". (til he's like the wind and drives off again into the sunset).
Certainly as a 14 year old watching it for the first time (which I still remember, I loved it so much and wore out the video tape) the message was not one about class distinctions for me but all about changing into a slinky sex kitten to win an aloof man. But you're entirely right, there's a lot more at play in this story, so I was being a bit unfair.