If choosing a Bayesian approach in a clinical trial can reduce the number of recruited subjects, I would imagine the pharma industry is strongly incentivized to adopt it.

Moreover you can manipulate your results by disingenuous prior choices, and the smaller sample you have the stronger this effect is. I am not sold on the FDA's ability to objectively and carefully review Bayesian research designs, especially given the current administration's wanton disregard for the public good.