> It is impossible to actually observe what would have happened, had there been no advertisement, because there in fact was an advertisement.

I can see how you would have that perspective as a third-party analyst of conversion.

It's actually easy to do if you are the exchange/sell-side provider of the advertising space. In your logic, where the advertiser requesting the incrementality study would have won the auction, just randomly remove their bid from some won auctions, have the second highest bidder win, and then track that user as the "control" for conversion purposes vs. users you did display the ad to. Voilà!

This is how Google in-house incrementality studies are run, for instance.