Even Amazon's ad servering systems don't seem to be told that I bought the lamp from them never mind some other store.
Maybe they are hoping I liked it so much I'd decide that I need another lamp, so they want to remind me where I got the first one from?
> is the most visible form is mostly what drove me to use an ad blocker
My reason for blocking ads was because of the increasing incidence of malware riddled ad hosts often being used by high(ish) profile sites.
imgur.com was the final bail of hay that made me install network-wide protection at home. I also rehost any image I decide to share from there, to protect people outside my LAN. I don't want the tech support workload of cleaning other people's machines after what I'd too often seen their (obviously not sufficiently verified) ad partners try to pull.
My privacy is fairly shot already, but at least I can try to protect myself and others from other malware.
It's possible that at the level of the ad network the products could be disambiguated, and then cancelled so that other companies did not waste ad spend. This would be difficult as the products would have different SKUs.
At the level of a single retailer, the retailer places a burn pixel on the checkout page which registers to no longer place ads for that product.
The pervasive tracking of which retargeting is the most visible form is mostly what drove me to use an ad blocker. I wonder if the cost effectiveness calculation factors in lost future purchases?