And in any sane company, the minute a product person says "oh this egregious error is a problem for some other department" they'd be fired immediately, so it still sounds like a useful exercise.

I'll be the first admit I don't have a ton of respect for the "product owner" role which has morphed largely into Tom Smykowski from Office Space[0] but the places I've seen them be actually effective and net positives for an organization are where they have the reach and authority to demand things like this be fixed, regardless of what department is "in charge." IMO a product owner who doesn't do this is refusing to do one of the few useful product owner roles.

[0] https://www.imdb.com/title/tt0151804/characters/nm0726223

Data tagging makes Walmart throw a huge banner ad for pancakes into your search for lentils?

Ideally, manufacturers and sellers would provide more, accurate information about products -- but I generally like how Google solved this within Google Maps via crowdsourcing by prompting users to answer questions about places (e.g. does this place have a wheelchair ramp?). I wish there was a better process to collect and store product information so it could be more easily shared.

Which would be flagged in the weekly review on the first week?

I’ve had good results with brute forcing tagging even when it’s not my job.

If I use my product and hate it, I make it better. Knowing they some other department sucks for years is no good.

I think all this boils down to companies not really giving a flip.

The product is bad. Shifting the blame around doesn't magically make the product better.