Author clearly doesn't appreciate that the ultimate truth of any authentication scheme is you should not trust anything from the user. So what if you take away a clients ability to specify what algorithm a piece of data is signed or encrypted with - if you blindly just accept whatever a client did and proceed then you're always gonna find yourself vulnerable.
Intel didn't use JWT tokens or pass a client header - they just trusted what the client sent and landed themselves in the same mess. I make the point to illustrate that what real security pros do is make sure basic checks like validating user input is done regardless of what specification or algorithm is involved.