The author of http://blog.intothesymmetry.com/2017/03/critical-vulnerabili... here FWIW. Personally I would not be so drastic. JOSE per se is not too bad (at least the idea is cool). Some crypto choices though have been really arguable...
That post is great work. Thanks again. But I think you're wrong about JWT. The problem with JWT/JOSE is that it's too complicated for what it does. It's a meta-standard capturing basically all of cryptography which, as you've ably observed (along with Matthew Green), was not written by or with cryptographers. Crypto vulnerabilities usually occur in the joinery of a protocol. JWT was written to maximize the amount of…
Using a public key algorithms makes also it easier to implement a sane key rollover strategy. I suspect this is the reason that Auth0 pushes their customers to validate tokens with public keys published on their JWKS endpoints.
As for X.509, I agree it kind of sucks but what are the alternatives?