Yes, and when he got there he put his feet up and closed his eyes.

https://youtu.be/0JQbeCAlF6s?t=61

What does it say about our culture that futuristic media envisioned flying cars and robotic servants but not an altered labor arrangement?

Modernism. Infatuation with the transformative power of technology. It transfers responsibilities of political participation (what it means to be a citizen) to a mechanistic, consumptive process (what it means to be a consumer). Could not exist without mass manufacturing (without which technology cannot fulfill its telos) or mass media (without which humans would not submit to this ideology).

It was a kid’s show. I doubt it was meant to be a cutting commentary on social structures.

And, while we are at it, what's up with the Flintstones and dinosaurs and humans living side by side. If that isn't commentary on the sorry state of academic culture I don't know what else is.

Flintstones is based in the future, not the past ;-)

Also, do cassowaries count as dinosaurs?

I'm not sure it says anything about our culture specifically. It speaks to all cultures.

The future is always going to be what we have now, but sexier in some way. So replace cars with flying ones, and replace work we do with robotic servants.

The really interesting science fiction doesn't do a linear extrapolation, it looks at how we might really change. But that's not what we get from a kid's cartoon.

Yes, that's what they're saying: that the Jetsons completely missed this prediction.