Why is riding a bike with a flat tire harder?

As a bike, or any vehicle with inflated wheels roll forward, the tire gets deformed, kinda squashed out. Scrunching up the rübber takes energy, and the more scrunching the more energy it steals. With a properly inflated tire the folds and waves of the tire is quite small, so there's not a lot of power lost. But with a flat tire the folds and deformation is bigger, and so is the energy loss.