It's a fair question. They don't need the blockchain until the money/nft leaves the platform. But to keep credibility, they'll need the NFTs to show up in on-chain addresses. They may end up only doing that on-request.
The NBA TopShot collectibles work on a blockchain, though the media being traded (NBA game clips) can only be seen on the official platform and you can't sell the collectibles on any other platform. And they're their own on-ramp by taking credit card purchases for the collectibles. As things stand, there's really no good reason for them to be on a blockchain at all, and personally I don't consider them to be a real NFT. None of that has stopped them from being successful, though.
I wonder if they even need the blockchain.