For the record, JWT is a payload and format spec for JWS/JOSE, which is really what you're complaining about. JWT is merely a claims set and an optional dot-notation serialization of a single signature.

JWT/JWS libraries that handle all the validation alone are treacherous. You should ALWAYS parse the JSON before hand, perform your claims and header(s) validation, and then pass the payload/header/signature. If anything, it's computationally less risky than running the signature blindly through a signature validation function and then checking the header.