I just watched this for the first time in forever and I think you're right!

New kid turns up in town and immediately hits on some guys girl and we're supposed to root for him? He's a scumbag.

A better film would be Miyagi kicking Kreese's ass, taking over the Cobra Kai and training those boys properly.

I don't think he knew the girl was "taken" before he hit on her. But he certainly was a whiny, ungrateful, entitled brat.