If you consider my perspective is that eBay / Amazon / et al are acting with the least amount of policing effort they can legally or financially commit, then yes, I would like to advocate that a marketplace such as eBay
should attempt to verify every item it sells is not counterfeit.
I'd like to avoid being unrealistic in that I don't think a marketplace can 100% verify every item and grow to scale, but I'm also extremely annoyed at the "all or nothing" kind of false dichotomy you've presented.
I'm not trying to be insulting or glib with the following, but if you'd like to peruse several different threads in this discussion it appears Amazon has more than enough reasonable data to address an issue, but has heretofore turned a blind-yet-financially-beneficial-in-principle-eye to the situation. If a bunch of humans sitting around and spit balling can hammer down a half-dozen examples and concerns out of altruism then I think any attempts of offloading that 'check and balance' into the Amazon system is quite significant.
If they get around to it, I'd classify their pragmatic motivation as akin to "I'm sorry your feelings were hurt" moreso than "What I did hurt you and was wrong."