Is it because when the electrons are excited to a higher energy level, they can lose energy and fall back down to lower energy levels? Due to the sheer number of antibonding MOs in the conduction band, this could mean that there are more levels for the electron to fall down to rather than instantly go back to the bonding MO, hence leading to more movement of electrons i.e. conduction of electricity?
Semiconductors conduct because some electrons are easily bumped into the conduction band
The basic definition of a semiconductor is a substance where there is an empty bundle of orbitals at an energy just a little higher than the valence band where the bonding electrons reside.
This gap is close enough to the valence band in energy that even thermal energy is enough to boost some electrons into the conduction band. This also explains why the properties of semiconductors are dependent on temperature.
But, when this happens, there are "holes" in the valence band as well as electrons in the conduction band. Both the holes and the electrons can carry current. Moreover, semiconductors can be doped by small amounts of other elements to either add electrons (n-type) or subtract electrons (p-type) from the material (this is vital in semiconductor manufacture for electronics). When doped, the balance of conductors between electrons and holes changes (n-type dominated by electrons, p-type by holes).
So the conductivity of semiconductors depends on a small number of electrons being in the conduction band. But the actual conduction happens by movement of both electrons in the conduction band and holes (the absence of electrons) in the valence band.