Lets say you have a legitimate website with uses form POST's or GET's to implement cross-site requests to some service on a different domain, authenticated through a cookie. This is vulnerable to cross-site request forging. Changing this to use fetch with CORS can protect against this kind of attack, since the service can now ensure the request is initiated from a legitimate origin.

It is just important to understand what CORS protect against and what it doesn't protect against. You can always forge a request to look exactly like a CORS-compliant request from a legitimate origin - but you still wouldn't have the necessary authentication cookie. If the attacker have somehow gotten access to the users cookie, then there is no need for request-forging in the first place, the attacker can just directly log into the service. If the users browser is compromised it is the same. So CORS protect against the specific scenario where a malicious site visited by a legitimate user forges a request to a legitimate site, misusing the authentication cookie associated with the legitimate domain. In this scenario, the CORS header will indicate the origin of the malicious site, and the server will be able to reject the request.