IMO large social media platforms are actually much more capable of running these experiments than academics. (Disclaimer: I work on ads at one of these companies).

Platforms can accurately determine who engaged with an ad (basic logging on their sites), they have infrastructure to create statistically balanced ad experiments, and can also accurately determine whether a conversion happened (either through a conversion pixel or through data brokers).

Running these tests on behalf of advertising clients, or for internal research is fairly standard. If we couldn't prove statistically that our ads were working, I would have left a long time ago.