"Middle class" is a term tailor-made to get workers thinking "well I'm not in the same boat as those people" and primed to punch down or pull the ladder up.

That's basically what I said in my last sentence, but at the same time you can't discount from a leftist perspective that some working class are poor and barely getting by while some working class are rather comfortable, and that those two groups have somewhat different material interests despite both being part of the working class. Of course that fact is definitely used to pit those two sections of the working class against each other to the benefit of the owning class.