There is a fan theory that Fallout lead to TES because of radiation. It holds about as much water as a sieve, but its fun.

It's been a long-ass time and some of the lore may have been retconned/clarified since then, however it was a conclusion I came to on my own. Basically, iirc, the Towers are hybrid physical/metaphysical structures which essentially keep Mundus (Nirn + other planes) stable and allow for things like magic to occur. When a tower is destroyed, Mundus becomes less stable and magical ability declines. Let's hope we don't destroy any towers then!

Oh wait. A bunch of the towers (are speculated to be) destroyed. Red Mountain (vvardenfell) was destroyed after the false-god Vivec lost his powers and could no longer keep the Ministry of Truth from smashing into the mountain, Walk-Brass zero-summed itself and the race that created it, the White-Gold tower was destroyed during the Oblivion Crisis, I don't remember what happened to Crystal-Like-Law but I'm pretty sure that's gone too.

If you wanted to get fancy with it, you could even point to the magic system getting less complex with each mainline game (yes, I know it's probably just laziness, but I like my explanation more). Hell, it seems like all the crazy, cool stuff happened long before the events of any of the games; it seems like all the races peaked before we ever got a glimpse into that universe.

So while I guess it's a bit premature to call TES post-apocalyptic, it's definitely headed in that direction. It seems to be a series about a world that's slowly collapsing and falling apart.

Edit: I spent some time trying to brush up on my TES lore (fuck, I'm starting to hear the games' siren song; it's been years), and came across this wonderful paragraph:

Using his dentition as tonal instruments, Anumaril dismantled his bones and built of them a Mundus-machine that mirrored Nirn and its planets. And when he had used all his substance in fangling this orrery, the Orrery of Elden Root, he placed the segment-sceptre within, hiding it between the Moons.

You... you did what?

I wish the games were half as interesting as the lore.

Edit 2: I remember why I thought it was post-apocalyptic! Space! Iirc all the races have been to space and had spaceships and space battles, except it seems like everyone has forgotten about it by the time the games take place. Combined with the gradual destruction of the Towers, it seems possible that the games could be post-apocalyptic but are being filtered through a lens of ignorance, making the residual advanced tech appear as though it's magic.

Oh man, you have no idea how deep the Elder Scrolls lore hole goes.