It's better for a browser feature the user has some control over to be the implementation point for this than incentivizing site owners to come up with novel tracking strategies.
Except this is not how things work. All you are doing is giving the advertisers another tool to track you, it won't magically make them stop using all the other ones.
I was thinking that they'd be forced to adopt this, as 3rd. party cookies goes away, but somehow I sense it's more likely that advertisers would adopt something like device fingerprinting instead.
The online shopping businesses really isn't interested in privacy, I don't even really blame the adtech industry for this one. The companies running the ads and retargetting campaigns want to know who clicked on what and when. Anything less will trigger a frantic search for ways to evade privacy improvements.
Device fingerprinting is a hack and unreliable in the long run. Third party cookies are being replaced with first party cookies and PII-based tracking methods like UID2, which enables a decentralized network of vendors to generate the same hash for the same email address across nodes, giving advertisers a global understanding of identity. Once third party cookies are gone, expect to see login prompts everywhere
