Competition is not always beneficial. Consider copyrights and patents. These are deliberate monopolies, i.e. huge restrictions on competition, in order to foster desirable economic outcomes.
As an example, if we eliminated pharmaceutical patents, this would enable greater "competition" in the pharmaceutical manufacturing industry, but guess what? Private companies would cease to invest in drug research. Meaning that, you, as the consumer, lose out on potentially new treatments being invented and brought to market.
There is a significant problem with the emergence of multiple-drug resistant infections. Even with patent protection, pharma companies are not pursuing development of new antibiotics. Why? Because the economics are unfavorable. Better to have a monopoly drug like Lipitor that people have to take for the rest of their lives than an antibiotic that you only take for two weeks .
Patent-protection does not necessarily provide solutions that markets want. It only provides solutions that are profitable with patent protection. There is clear market failure regarding antibiotics. Where are the desirable economic outcomes and new treatments?
Appealing to the pharma industry as an example of where patents work at their best is not helpful for a discussion on patents unless you identify its obvious shortcomings.
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.