There isn't a good non-technical answer to your previous question but lemma 3.3 of this paper [1] says that if you can correct a finite set of errors for each qubit individually then you can also (essentially for free) correct all other errors. Specifically if you correct a set of errors which spans the set of possible errors (for example the Pauli errors on each qubit do this) then you correct all errors.

This is essentially the reason people are still interested in quantum computing, and why quantum error correction is viable at all. You can protect highly entangled crazy states from highly non-local complicated errors using only the resources needed to correct simple local errors.

[1] Key ideas in quantum error correction, Raussendorf 2012: https://royalsocietypublishing.org/doi/10.1098/rsta.2011.049...