Perhaps if the compression cycle was integrated with
braking, then useable energy could be recovered and
used again. ??
The problem is that all regenerative breaking systems add weight, complexity and require additional energy and materials to manufacture and eventually service. Those have to be considered and they are the things that proponents always leave out as they are all net loss.
The added weight means more energy is needed to move the car than if it was not there. And so little energy is regenerated that you cannot come close to getting a reasonable tradeoff.