Yes, you do in fact need CORS to set the arbitrary header in the example if it's even possible to send from a browser. I suppose it might be possible to send as `HELP xss:` which is close
Like you said, you can send requests, but not the one listed in the example and you're severely limited in cross protocol interactions to valid http where you don't need to receive a response... (which some of the example attacks require btw)
I think this is an interesting issue to consider, but the examples are based on wildly different threat models that include TLS being hijacked, maybe DNS if it was performed with rebinding, the FTP server being hijacked for one of the attacks. It is not at all concrete. Interesting, but not really worth worrying about.
The interesting cross protocol attacks that I've seen involved SSRF talking to memcached, as a classic example. Something private. In practice I think they would struggle to find a single real world instance where they can pull off an attack enabled by this behavior. Which is fine, it's academic. Just not what I expected given the coverage.