For example, AS::ME relies on shared secrets, which I think makes it unfit for distributed systems. Implementing JWK with asymmetric keys can really reduce provisioning and configuration costs. Keeping the signing secret on one private, hardened auth server (or cluster) also allows smart things like automated key rotation.
2. 100%. There's at least one right way to do JWT, but more ways to do JWT wrong.
3. JWT et al provide a fine starting point, I don't see a reason to start from scratch.
I'm not tied to the JWT spec, but I'm quite happy with what I've been able to accomplish using a careful implementation in my AuthN server: https://github.com/keratin/authn