Why Can Tight-Binding and DFT Models Assume Electrons are Non-Interacting?

[Nusc]

What is the justification behind tight-binding, nearly free electron drude model, to assume electrons as non-interacting? Because it is clearly not the case when considering coloumbic interactions, why can these models do this? Coloumbic interactions are strong so I wouldn't consider them to be idealized.

Or why is density functional theory valid? How is it still valid by expressing things in terms of its electron density while neglecting couloumbic interactions?

 

[Nusc]

Nevermind I understand now.