I hope you meant, "If you want to pass any secure information that would require HTTPS you can't use it.". POST does not make anything "more secure". (And JSONP should work cross site with HTTPS anyway)
Of course if you want to do multipart submissions or anything too long to fit in a url, you'll be needing POST anyway.
As a general note, GET and POST requests expose their parameters with equal visibility. It's just that the browser makes it more obvious what your GET parameters are
Of course if you want to do multipart submissions or anything too long to fit in a url, you'll be needing POST anyway.