Fortunately, the attack is limited by the fact that the attacker can't see the response from the server. If the attacker could view the response, it would break CSRF protection based on nonces as well.
No, but that wasn't my point. My point was that this vulnerability can be (and has been) worked around by using nonces in the header. If you can see the response body, that protection becomes worthless as well (and there is no workaround for that).