Statistically reliable purchases studies are very challenging. People have multiple credit cards and sometimes pay cash. If you are buying a car you don't put it on the credit card. Additionally, you have multiple cookies/MAIDS that may or may not be associate with the same person/credit card. Even companies with Google or Facebook resources can't get this to work reliably. If it is a direct response advertiser, of course, you tell Google/Facebook that a purchase is made, but these advertisers are not the bulk of the market and many advertisers don't want to give Google that data.

Because reconciliation across sessions and platforms is non-trivial. Especially with browsers become increasingly adversarial (aka pro-privacy).

https://www.quora.com/How-can-I-reconcile-Facebook-advertisi...