This would be the solution for any problem/algorithm, wouldn't it?

Factorize big numbers, sort an array, beat stockfish at chess, create a SOTA microkernel OS from English description. All O(1) with lookup table!

It's not how complexity works.

The model usually measures in terms of fixed-size operations, e.g. 2-input binary gates. There's some variation in how to count memory lookups, but even in models where accessing a large memory counts as only one step, any tables present in the code still have to be fixed-size (except in models like P/poly, but even then they can't be exponential size).

An algorithm is a finite sequence of instructions, and so can't include an infinite table. More generally, https://en.wikipedia.org/wiki/Effective_method

because you're looking up a result not solving for it