In the tight binding model, it's said that in a certain limit, we can regard electrons in the solid as localized to individual atoms. This statement shows up in most introductory condensed matter textbooks, like Ashcroft and Mermin, Kittel, and Altland and Simons.
However, the statement is basis-dependent! If we expand in the Wannier basis, then it's true that our electron wavefunctions are each localized about a particular atom. However, we can also expand in the Bloch basis, in which case "the" wavefunction of each electron is delocalized. Moreover the Bloch basis feels more natural to me since it diagonalizes the Hamiltonian.
The equivalence of these two perspectives follows from second quantization, as you can write the second-quantized ground state of the system in terms of creation operators in either basis. Hence there's no basis-independent meaning of "the" state of a single electron. How can localization be defined in a basis-independent way?