[tomrod]

Causal inference has made a lot of improvements since WWII, and "if" the advertising company knows what they are doing they run effective A/B or MAB testing; that said, statistical power is typically low because of insufficient sample size for individual companies.

You could pool all ads together, but since each advertising company is independent you get into all kinds of weird path dependencies.

While I wouldn't claim to be an adtech practitioner, I did at one point help a few F500 work through conceptual models of multitouch attribution and other statistical issues. These are very nontrivial issues -- proving advertising effectiveness is very difficult!