So, if the merchant failed to implement this, Google would never know to stop showing the ad.
There is a theoretical justification for that (note: "theory" not used in the scientific sense!) -- for large ticket items like cars, recent buyers are more likely to notice an ad for the expensive item they just bought. Some ads are aimed at them to make the whole "experience" somehow better, to offset buyer's remorse. That way you will talk up your purchase and be more likely to buy another when you replace it.
The other is when you have a high volume low-price item (e.g. toothpaste): you've demonstrated a willingness to buy (i.e. you're a qualified buyer at some level) so why not try to remind you that the next time you need toothpaste you should get it from the same place?
Since so much marketing "science" is bull, nobody actually knows if this works (any more than they do with the online ads). But at least your seeing these time-wasting ads is intentional, rather than necessarily a software error.
Thus in my last sentence I was generalizing to say that marketing, even formal marketing analysis with statistics and A/B models, is still a mixture of heuristics, data, and superstition. And its practitioners
Since it's a kind of social science, I say that in contrast to fields like economics and psychology which also have plenty of charlatans but whose major practitioners are well aware of, and discuss, the epistemological flaws that still remain in the foundations of the fields. By comparison most marketing "theoreticians" remind me, at best, of alchemists.
There's no question that marketing is crucial to any successful business. But we have to realize that it's typically simply just gut judgement.
In any case, there's plenty of exact science in marketing dealing with statistical modeling. Then you have pricing, which is arguably the biggest part of marketing (a lot of people don't realize how much thinking goes into a pricing strategy). Then you have communication in all of its marketing forms, and lastly you have the product creation, which in itself is part of the marketing.
I view it like operating a jet. I have access to lots of buttons, switches and dials, and I know the science that takes care of what's beneath them. But in the end, I'm only interested in what happens as a result of using them.
Now? That one minute websearch will stay with me for weeks as people push ads for things that I have no use for.
Prosthetic testicles for dogs; specific terms used for bras; packers and binders - my search history gives me a variety of eye-popping adverts.
Also: they really need to let people opt out of some advertising. People with alcoholism might not want any alcohol; people with OCD might not want cleaning products on a TVOD page about OCD (real example. I'd post an image but it's on the other computer).