As experiments go, this would be a fairly easy one to conduct. If Nike wants people to know just how much faster (if at all) the shoes are than others, they will fund an independent study. But perhaps too much precision wouldn't be as good for sales as the mystique surrounding the shoes now.
The simplest study would just take 200 volunteers from a large university and split them evenly between treatment and control. The goal would be for 1 in 200 students in a school of 40,000, to be willing and able to run a fast distance race. They would not be told the real purpose of the study, rather they would be told something like, we want to film fast runners wearing this shoe to study differences in wear patterns across runners in order to improve the design. You will need to run as fast as you can for 10 (or 20) miles. Perhaps run a second race a week later and offer a bonus for every 10 seconds faster they run the second time, switching the treatment and control.
That alone would produce excellent evidence. But there are various things that could be done to improve the quality of the estimates (propensity score methods to improve randomization, modeling covariates like prior PR). You could try to get at placebo effects by asking the runners if they have ever heard of "Vaporfly" or to rank a list of shoes in terms of their speediness. For a subset of runners who have no opinion, you could randomly tell them that their shoe uses new technology that makes them 5% faster.