You don't use the blockchain to verify ownership of a private key. You know the public key, and the owner of the private key can sign any message to prove that they indeed have the private key associated with that public key. This can be done completely offline.
Isn't a crypto wallet, literally a key pair, the purest form of identity verification? It's something you have (private key) and something you know (passphrase). No need for some central authority, no need for privacy concerns.
You are right on the latter point, a keypair itself is a pretty good method to verify pseudonymous identity.
However, we are talking about NFTs as tickets. Traditional ticketing relies on secrecy, or in other words possession of ticked-id grants entry. Data embedded in NFTs is (and has to be) public, therefore token auth model does not work, you must use challenge-response model. The very point here is that ticket data has to be linked with a keypair and provided at the moment of sale to be verified upon entry. Public key must be provided at moment of sale, blockchains are one way to store that link, private database of ticketing system is another. Blockchains bring their own disadvantages and the only advantage is trustless transfer.
In what scenario trustless pseudonymous transfer of a ticket is an advantage worth disadvantages of the blockchain.
Isn't a crypto wallet, literally a key pair, the purest form of identity verification? It's something you have (private key) and something you know (passphrase). No need for some central authority, no need for privacy concerns.