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Some people still believe there are no politics in Star Trek
(startrek.website)
As powerful as this scene was, the next one has Rom asking his mom to get naked. Ferengis are the best!
Most of the other series were more philosophical. It wasn't really about the long-lasting impacts of politics, rather more just thought problems that were wiped away at the end of the episode.
I think that's what OP meant when they said "...politics in ways the other series never did".
Also, to put it more simply.
When faced with Q, Picard tried to reason against an unreasonable foe using philosophy. (theory)
When faced with Q, Sisko punched him. (praxis)