So, I can almost guarantee the initial premise of 'futurama' was 'animated star trek, but incredibly low stakes and played for laughs'

Except they couldn't do it as star trek, so it had to be its own thing. Maybe it would always have been IRS own thing, and the writers knew this.

20 years later they actually did 'animated star trek, but low stakes, played for laughs'. And it was good! I enjoyed it!

But even with the benefit of a more permissive format and two decades comedic distance, 'the lower decks' only holds a candle to 'futurama'. 'The lower decks' was shackled to existing versions of the story, their storytelling conventions, and their setting lore. 'Star trek' has to be post scarcity, has to be at least broadly Utopian, and centers around the fundamentally well intentioned usually competent always hierarchally organized 'big good' organization of the setting.

'Futurama' can have a sewer mutant who thinks she's a mystery alien because her mom had a PhD in linguistics, a billionaire heiress who's slumming it, a completely inane bureaucrat, and a robot devil who lives in new jersey. They can layer in deeper meta-jokes, like bender subtly actually being the greatest bender unit ever made because they're doing the world building from scratch, and can generally be meaner to/about their characters than anyone tied to 'star trek' would ever be allowed.