"Publish -> people find insight and try to pick it apart -> You either have flaws or you get reproduced... Only then should your paper be of any worth to be quoted or sighted from."

This is already how it's supposed to work. The review before publication is a fairly superficial check that just confirms that what you describe follows basic scientific practices. There is no validation of the actual research. A proper reproduction is what's supposed to come after publication.

IMO the real problems are that a) there isn't much glamour and funding for reproducing other's studies and b) "science journalists", university PR departments and now in part people on social media are picking up research before people on the field looked at it or misrepresent it. Suddenly the audience is a lot of folks who never were the intended audience of the process.