This is one big issue I see with current NFTs to be honest. Even though they're 'blockchain-backed', they seem to require (centralised?) marketplace websites to be able to trade them. How is it possible that BBGC's 'Bitcoin Blockchain Gold Coin' project went down together with a single website (ascribe) going down?
That doesn't seem to align very much with Bitcoin spirit to me. Way too much trust involved.

An analogy would be if you had the rights to the Mona Lisa, but couldn't prove or transfer them anymore due to one website shutting down due to interest in art ownership proofs dipping down for a couple years.

In my mind, coloured coins would be much simpler and much less reliant on such websites. Since the utxo is 'tainted', you could transfer it like any other Bitcoin transaction (e.g. with dust limit amount) even without any NFT explorer or marketplace. Just with your regular wallet app / software. And 'NFT browser' could be implemented client-side; showing a received transaction indeed contains a coin coloured in a way that proves ownership to X - as well as in any regular online- or self-hosted block explorer.