If the table size is constant, no matter how large, then it is correct and important (even if useless; the existing n*log(n) algorithm is already useless).

I honestly think there’s a lot of fuzziness possible in complexity theory because of things like this. Yes you can skip some portions of a calculation and rightfully so by the current established formalisation of complexity theory but i think under another formalisation we’d probably see these nlogn^0.999999 cases become more clearly nlogn.

Cf. Blums speedup theorem for an extreme example of this

Just because something is proven and shown to be true doesn't mean that it's always practical.

The proof can be entirely valid even if it's not actually reasonable to implement and requires an enormous size lookup table - but it still is a meaningful mathematical result and makes progress.

I'm sure there are plenty of times where originally something was proven and thought to be completely impractical but then later had niche use cases or was the bedrock for solving other cases. And the opposite is true: there remain plenty of proofs of things that are mathematically certain but will in all practicality never be useful.

Exactly, big O doesn’t claim it’s actually faster in practice on a computer for all inputs