On skates you push with the skate against the ground to accelerate. If you had spring you would first need to press against the spring and then against the ground to do the same acceleration. So it would be a lot harder or slower. On a skateboard you push with the leg that isnt on the board so there also isnt a bouncy thing in between. And for bikes there is also nothing to compensate between the pedals and the wheel.
Specifically roller or quad skates, they have rubber or some type of polyurethane “cushion” which acts as a damper and allows the truck to flex. It’s similar to a skateboard but they typically have a more angled geometry to the plate. The plate itself needs to be ridged in order to transfer the push energy to speed. If there was flex, they would be less efficient.
Everyone asserting that pushing off would be less efficient needs to go back and check their physics knowledge. The entire point of a spring is that very little energy is lost in its action. In any case, the spring constant would be chosen to minimize compression on push-off. The answer is really that springs give no benefit in most uses of in-line or roller skates. Springs would be nice in in large wheel off-road inline skates, though.
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