And yet, it’s been done:

In a First, Randomized Study Shows That Masks Reduce COVID-19 Infections

A large study co-authored by Yale SOM’s Jason Abaluck and Mushfiq Mobarak tested the effectiveness of a mask-promotion program in Bangladesh in increasing mask use and preventing symptomatic infections. The study found that masks significantly lower symptomatic infections, especially among older people and when surgical masks [instead of cloth] are used.

https://insights.som.yale.edu/insights/in-first-randomized-s...