Watch the talk at the bottom of the page. JWT/JOSE are chock full of dangerous footguns that aren't just theoretical, they have repeatedly been shown to be poorly designed and too risky to implement correctly as written. Using fewer, known secure cryptographic primitives as part of the spec ensures it's impossible to get the security wrong, can't be misused.
The point is that the JWT spec leaves it open to the implementer which primitives to use, which invites bad implementations to be insecure. PASETO requires a small subset of known secure primitives, preventing that problem altogether. It's not "just nonsense".
The JWT spec can thus be fixed by changing the recommended set of primitives. No need to reinvent the wheel with custom serialization (that probably also has vulnerabilities when implemented by clueless people).
You parade the alg=none vulnerability that has been fixed long ago as the reason to reinvent the world. It's simply not.
You keep repeating that. What is "fundamentally flawed"?
PASETO has exactly the same vulnerabilities. You can specify a different version, and a buggy implementation can misinterpret it. With PASETO, the algorithm selection is fully under the control of the attacker.