As far as I know, nobody has published any hard data that quantifies any energy lost from flexing a shoe sole. Any minute deflection within the elastic range of the material comes back into the system. As far as weight, where do you get the 1/4 lb (110 grams) on each foot? All shoes I've seen lately range in weight from around 460 to 500 grams/pair. That's 20 grams/shoe, or about 0.04 lb per shoe. Far from the number you quoted. That 20 grams per shoe is minimal.
If you want to split hairs and quote physics as your rationale, go ahead, but in reality, I'm staying with negligible or no difference