If the band theory is complete right, or in other words, if we have indeed free electrons, then there cannot be exciton. We just fill the energy levels.
In other words, in a tight-binding model, we cannot get binding between an electron in the conduction band and a hole in the valence band.
Only in a realistic material, where the model is not a whole story, can we get the exciton, right? But what exactly is missed by the tight-binding model? This is not clear in textbooks.