I think both you and GP are somewhat misrepresenting the OP is saying. OP's argument is three-fold:
1. JWTs are not a good fit for a session token (although there are several RFCs that are trying to shoe-horn JWTs into this use).
> TLDR: JWTs should not be used for keeping your user logged in. They are not designed for this purpose, they are not secure, and there is a much better tool which is designed for it: regular cookie sessions.
2. JWTs have other "valid" use cases that only need a very short-lived token (e.g. a transit token or a request signature) and don't need to care about user authentication, revocation, XSS etc.
3. But JWT should not be used even for the "valid" use cases, since you have better (read: less outrageously insecure) alternatives nowadays.
> Also note that "valid" usecases for JWTs at the end of the video can also be easily handled by other, better, and more secure tools. Specifically, PASETO
You've noted these issues yourself. There are many common vulnerabilities with JWT: alg=none, algorithm confusion and weak key brute-forcing, mandating weaker algorithms like RSA and ECDSA while making the best, fastest and easiest to implement algorithms like EdDSA "optional".
There are also other design deficiencies that JWT makes by trying to be a generic cryptographic envelope format rather than a token format: e.g. expiration can be omitted and this feature that caused some libraries to not verify expiration by default or have a different (and confusing) set of token parsing methods that do not enforce the expiry. PASETO is a better design that is secure against all of these issues. Sure, there are a few minor qualms I can find with PASETO (e.g. no mandatory key ID and no support for non-JSON payloads), but it's unlikely to face the same avalanche of CVEs we got with JWT libraries.