ever bend some metal over and over to break it. Notice it gets hot. That is energy dissipated from bending. When you petal the bike, and the frame flexes, which has to happen, some of your energy is going to heating the frame. Not enough to feel, but it is still gone. Bike with suspension, as the shocks give, it heats the oil in them, one of the reasons a mountain bike is harder to petal. That is why the elite bike have lock outs for the climb and then full suspension for the descents.
Of course our bodies would not like a completely stiff bike. the vibration and shock would be horrible. So we want the frame to have some give when transferring wheel shock to the bars and the seat. But when pedaling, there is a twisting force to the bottom bracket, movement here is wasted energy so we try to minimize it.
We are low powered motors, so every last bit of power we want to put into locomotion.
Rod