Tldr (edit I did actually read) it's subjective, yes. Descriptors of genres aren't objective facts. Entirely my point. Well elaborated.

But I'm pointing out that if some random teen came up to you to ask for suggestions of "post-apocalyptic shows", I'm pretty sure you know they would be disappointed when watching Picard having tea and discussing philosophy when all they wanted to was half-naked people in leather duking it out in a blood-dome, you know?

I'd that Dredd is considered that post-apocalyptic by people's who don't really know the canon. More like dystopian future. But hey, like I said, subjective terms. Use them how you think best.

I'd agree calling ST "post-dystopian", perhaps. And I'm not arguing that people diegetically would not have thought "the world to have ended", but again, subjective, imo.