Well let's be clear, the "trade-in anything" day was a fancy discount day. They gave everybody $5 for whatever they brought in, online you can read from employees that they just donated or threw it all away, no attempt to actually keep any of it to sell.

That said IMO the biggest difference in the two situations you're describing is that EBay is not in the business of buying the items to then sell later, they just facilitate transactions between two parties and some of the logistics (depending on the seller). They're similar as far as dealing with "used goods" but the actual design of the business and risk being taken on is very different.

EBay also not really lacking what you're describing - there are fufillment centers that can be used for EBay listings, there's the EBay "Authenticity Guarantee" program for cards, they already own TCGplayer which does all of this for trading cards way better than GameStop does, etc.

Perhaps somehow these things could be improved by GameStop but I can't imagine it being significantly better than it currently is.

They are wildly different businesses. Ebay is not in the business of holding physical goods, they are a marketplace that connects buys, sellers, and shippers and adjudicates fraud, collects funds, handles taxes, etc. They are not a warehouse.

Gatestop is a retail operation that buys and sells goods. It takes on all the liability for fake products, it puts capital on the line to purchase used goods, it is a totally different (and worse) business