CORS prevents reading from a resource, not from sending the request.
If you find that surprising, think about that the JS could also have for example created a form with the vote page as the target and clicked on the submit button. All completely unrelated to CORS.
CORS does nothing of the sort. It does the exact opposite – it’s explicitly designed to allow reading a resource, where the SOP would ordinarily deny it.
CORS is a lot less strict around GET as it is supposed to be safe.