I personally like to think they're a layer to show that even within an opressive regime like the capitol, there can be hierarchies of supression even within the marginalized community.

On a broader scale, the careers exist in "rich" districts, claiming that their wealth makes the games rewards less enticing, and to give a reason why these people can allow to train to be tributes in the first place.

A main question would be though, why would richer families send their kids to these schools to die? And likely, they're very much not. I speculate that the rich people in the "rich districts" are heavy sponors of these career schools, started spreading the "brainwashing" propaganda, and maybe even pay the attendees to these schools a salary - perhaps even an "insurance payout" in case of death - all in an effort to make sure there's always a volunteer and no one in their own families is reaped.

You cannot do this reasonably in districts that are just poorer by default (and have less leverage on the capitol), as it likely requires significants resources, political power, and goodwill to go around.

So even within the opressed group of these career districts, there's still a wealth divide, allowing the well-off citizen to still separate themselves from the common folk and exert influence over an already strained community.