Something like this is being messed around with by a few different companies in the form of fractional share ownership in cards, which is likely to be the form it ends up taking (a trusted market, ala the Nasdaq).

So the market holds the 1952 Mickey Mantle and shares get issued against it. You can buy and sell the shares, you never need worry about taking possession of the underlying asset. The market holds the physical asset and insures it.

If cards are going to have another level up from the single digit million dollar area, it'll be due to fractional ownership speculation. Up to this point, generally speaking, either a singular or very small number of people own the most expensive cards or can afford to own them. With fractional ownership, people can put $500 into a $5 million Mantle card, and own part of its appreciation over time. That flood of buyer demand will inevitably pop the total value of all the shares far higher than would otherwise occur for the card as a whole (which prompts the question of whether $30-$50 million type valuations end up happening for some of those cards, as in the art world).

PWCC is one of the obvious candidates for building a giant holding market, with card IPOs or something akin to that. They already allow you to borrow against the cards you hold in their vault. I'd be surprised if they don't experiment with fractional ownership in the near future.

I had this exact same idea not long ago but with PSA graded Pokemon cards. Essentially a reserve for digitising real world assets and collectibles. The challenge would be convincing everyone that your reserves are always secure and properly backed.

Why burn the NFT? Wouldn't it be better to transfer the ownership of the NFT along with the physical item?

That gets back to crazygringo's point that someone down the line could sell the NFT paired with a counterfeit physical item and it might even be hard to tell who is the scammer and who is the victim.

Doesn't sound very liquid relying on a single person to follow through on that.

The NFT can be traded infinitely as fast as the network will allow you. You would only have the NFT burned if you want to redeem it for the underlying asset.