The proposal isn't "springs under your feet" it's "springs along your legs that you load while your leg is in the air". The point is that by loading the spring with a leg which is otherwise not doing anything you're able to increase the overall energy output of the body. Their Fig. 2 shows exactly the (theoretical) difference between the naive "jumping stilts" approach and what they're suggesting.
> Cycling is faster than running partly because (i) the rolling motion of the wheels prevents collisional energy losses from stepping but also because (ii) wheels can support the weight of the body in place of the legs, while (iii) pedals enable the human to supply energy continuously in the air instead of intermittently when the leg is on the ground .
Super interesting to see that they still can't outperform cycling. Presumably their proposal resolves most or all of point (iii), so the difference is from (i-ii). I would assume that, of these, (ii) would be the hardest to replace with any kind of leg attachment