If heads of product were forced to use their own products for a full afternoon every week the quality of the web would increase a lot. The amount of high level product people that can't demo their own product and cannot find features they hype up in slide decks is depressing.
Not disagreeing, but this example seems like a data/tagging problem which is probably some other department.
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