I can’t prove this in physics term but here is my theory- springs no doubt help you jump higher in the air than what you will accomplish without them, however they don’t help you run faster horizontally. While jumping on a trampoline the more height you gain, the more time you lose on the ground, so if your aim is to get maximum height on each bounce a spring is better than no spring. However if your aim is horizontal speed, you need a combination of maximum power to the ground in minimum ground contact time and springs would damage the time aspect in the equation. So you might get longer strides but slower cadence and slower speed overall. Shoe cushioning be it foam or carbon helps in one aspect it softens the impact and the pain to the bones and joints and also damage to the skin of your foot, this might be helpful when you ran long distance, but it doesn’t make you faster or spend less energy. That’s why short distances are run on hard surfaces with minimal friction- that’s why they wear spikes- with minimal ground contact time with powerful impacts