Before you call something pseudo-science, you must first be qualified to understand the real science.
Efficiency is relative. It is easy to see how inefficient running is compared to other forms of self-propelled locomotion, like roller blading and cycling. How much do roller blades weigh? Typically 2-5 pounds, compared to the 5 oz. Adizero Pro shoe. Adding these heavy weights on the feet of a marathoner allowed one to cover the distance in 56:45, last year in Berlin. If several millions of years of evolution produced optimal efficiency, cars would be built with mechanical legs.
If shoes don't make you go faster, why wouldn't more elite runners opt to run barefoot, like Zola Budd and Abebe Bikila, instead of opting for shoes that cost $200-$500? After all, runners will do everything it takes to go faster, and wearing no shoes is completely legal and available to everyone at no cost.
Energy is lost in everything that bends or compresses, from the hips to the knees to the ankles to the toes, and all the muscles and tendons in between, as well as the soles and cushioning of the shoes, if that energy is in a direction other than causing forward motion. Each foot landing acts as a brake as kinetic energy is directed downwards rather than forward. Most of the energy used in running is to compensate for the lost energy, rather than propel the runner forward. Older shoes designed to reduce impact uses a foam which absorbs the energy which then dissipates in all directions, making them less efficient than shoes which absorb that energy, and then dissipate the energy back up to the foot on the rebound.
The running shoe was invented a long time ago. Running shoe technology has advanced over the last 60 years, as new lightweight and rigid materials were developed, compared to the golden oldie days when shoemakers cobbled together leather and rubber. The latest technology puts a thick layer of lightweight foam on a rigid carbon fiber plate, capturing more of that energy and rebounding it at lift-off in a forward direction.
When you speak of horse racing, you just introduce yet another topic where you are clearly clueless. A quick search shows that horse racing today has the very same doping issues as athletics. It is arguable worse, as the welfare of the horse is not given much consideration, and anti-doping isn't as organized and uniform worldwide. Declaring no significant progress in the last half-century despite all the alleged advances in doping, is consistent with what we have seen in distance running since the mid-1980s, among the matured non-Africans -- until the era of new shoes. The requirements and constraints of putting shoes on horses are different, as their hooves are not like a human foot with toes and tendons and fascia, but it is no less scientific, as horseshoes are also made of different materials and specialized to perform different functions, from racing, to increased traction, to correcting its gait, and for injury rehabilitation.