You know why we cannot find new antibiotics class? Because it is hard, really really hard! Your statement about economics being the main drive of finding new cures, including antibiotics, is a great insult to tens of thousands of researchers working hard day to day with the sole purpose of find that damn compound. Yeah, these researchers are human with lots of feelings and sometimes with friends and families needing new treatment too, and they are not just working for the salary or bonus.
Patent system is not perfect, but getting rid of patent system will not speed up or better incentivize any effort of finding new drugs and cure. Think more public funding in basic research in universities, and new/better way of regulation/approval instead.