What is wrong with trade secrets anyway? It's not like someone who discovered something is obligated to reveal it to the world. If he chooses to do so out of his good will, fine. But if trade secrets remain despite patent system, that can only mean patent system is not fully enforceable yet.
Trade secrets remain today, mostly over the things that aren't (or aren't likely) patentable. So even perfectly enforceable patents would make trade secrets go away.