Why is the resonance concept not required in molecular orbital theory?
Because MO is closer to reality.

Resonance is a convenient fiction used to simplify the visualization of some molecules, and rationalize their actions in the frame work of Lewis structures. But every resonance structure you have ever seen in your life is a lie. 

Well, this is not exactly true. It's more precise to say that resonance structures are like blind men trying to describe an elephant: they each give a partial snapshot of truth while being wholly inadequate to describing it all. The "true" structure is a weighted average of all the resonance structures based on how stable they would be if they were the actual molecule. 

MO cuts to the chase and attempts to directly describe the molecule in terms of its molecular orbitals: another convenient fiction, mind, but one that is closer to the truth. The reason you don't need "resonance" MO structures is because molecular orbitals are inherently a probabilistic construct: they already take into account the uncertainty in the electrons' positions.