> Public key cryptography can be used with JWT tokens but they don't solve the problem of how the client will generate key pairs, demonstrate proof of possession of the private key, and enrol the public key with the API.
JWT is not in any way attempting to solve the problem of client identity and authentication. Rather, the question of federated user identity and how to validate that the identity assertion came from a trusted source (where the PKI and assertion signing comes in).
Furthermore it is signed with, among other assertions, the audience assertion so that you can cryptographically verify that a token was given with the authorization of a user by a trusted service (your JWT provider, via whatever authN methods it allows) and to a given client. This should give a substantial enough audit trail to enable reasonable proof that an end-user authorized a client (which itself had to authenticate to the provider) to perform an API transaction if it can be proven that the signature was validated and that the token issuer was clear about exactly what the user was giving the client authorization to do.
OAuth2, OIDC, and all modern standards I'm aware of also require client validation of some form. From the OAuth2 spec:
Confidential clients are typically issued (or establish) a set of
client credentials used for authenticating with the authorization
server (e.g., password, public/private key pair).
If your goal is to provide a non-repudiable audit trail of user identity and authorization and client identity and agency (authorized by the user to perform X) then OIDC, JWT, and client AuthN via request signing with registered keys should be more than sufficient to avoid liability in the case of rogue clients or shady users. As always, the audit trail is the most important piece, along with sound crypto and standard practices that have been audited by appropriate experts, so that your audit evidence cannot be reasonably called into question.