Indeed, user embedded pictures can fire GET requests while can not make POST requests. But this is not a problem if you don't allow users to embed pictures, or you authenticate the GET request somehow. Anyway GET requests are just fine.
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.