The typical example in favor of patents is that of drug discovery: it's expensive to conduct but a drug is trivial to copy once approved. Since the FDA is the govt entity mandating the trials (which is a substantial portion of the time and cost), why not let the FDA itself grant exclusive approvals to drugs for n years? E.g. approve only Lipitor (Pfizer's brand) for 7 years, and then approve Atorvastatin (the chemical).
Other regulated industries could do the same: the regulatory body offers the temporary monopoly to incentivize innovation. Are there any unregulated industries where patents are critical to innovation?
The quid pro quo for patents is a short term (17 year) monopoly to the inventor in trade for adequate documentation so that the invention can be generally exploited and used after the monopoly period has passed. Your proposal seems to have a different view of what the role of patents is (or should be).