Then you can make the form make post requests by changing a method. Nothing wrong with this either -- the browser will navigate there and serve the page to user, not to the origin server.
What makes it problematic is the combination of cookies from the destination domain and programmatic input or hidden field from the origin domain. But the only problem it can cause is the side-effects that POST request causes on the back end, as it again doesn't let the origin page to read the result (i.e. content doesn't cross the domain boundary).
Now in the world on JS applications that make requests on behalf of the user without any input and backend servers acting on POST requests as user input, the previously ignored side-effects are the main use and are a much bigger problem.