Are the sports team in the US which still reflect the socio-economic background of people in that city/ area?

Not really, but I think the branding of some teams plays off of the area they represent.

Steelers are branded on defense and hard-nose physical football, akin to the working class populace they represent. Milwaukee Bucks and Buffalo Bills take on the persona of their small metro regions - often forgotten about on a national level, leading to some chip-on-their-shoulder type stuff. "Showtime" Lakers out of LA adopting a sort of Hollywood persona, etc.

Interesting to wonder whether it's a personal thing of me seeing these teams through the lens of my own personal bias of how I view their markets - perhaps there is no correlation and I'm making it all up. But I do think team branding often leans into those types of tropes in order to connect more with their fanbase.

/r/AskAnAmerican Thread