<Search for something specific like "white nike hightops" and maybe 30% of the results will be what you are looking for.>

While I understand your frustration, there is an explanation. You are thinking of search & filtering as some sort of mathematical / boolean algebra process (hey, it's ok, I'm a CS grad).

Amazon is thinking about it as, "what does our show show that customers who have searched for [white nike hightops] have actually purchased in the past?" This is their search fitness function and they don't think they are wrong.

I agree on the broader point that 3p sellers and counterfeit products along with spam listings are a mess.

You may be assuming intent where there is really only incompetence

<Former Amazon employee, although not in search. It's intent.>

I think Google is failing here really. They should be able to find the exact product. I should be able to click on an image, and select "Find stores in my area selling this product", or they could find a nearby internet shop so shipping is fast. They should be able to replicate the same experience as Amazon, and make it better, and apply it to the whole internet.

I don't understand what is taking Google so long to figure this out. This is where the money seems to be.

(Otoh ... maybe they are afraid of becoming too large.)

>I think Google is failing here really. They should be able to find the exact product. I should be able to click on an image, and select "Find stores in my area selling this product

Google already does that. At least in my area. Type in a search. Click "Shopping" and it shows stores nearby that could have the item. It's not 100% perfect because it'll be decades before retailers allow Google to monitor their inventory in real-time, but it at least gives me leads, especially when I'm in an unfamiliar city.