A patent is granted for the invention of a drug, not the testing. If the monopoly were tied to the approval process, it would be limited to the country where the approval was granted. So shepherding a drug through the FDA approval process would get you a monopoly in the US, but not other countries.

Also, you can patent drugs that haven't been approved, which makes it basically impossible for anyone else to do the clinical trials. Breaking the link between the research and the approval process would make it easier for effective drugs to get tested and approved.

Finally, sure, that scheme would be a lot like patents. But at the very least it would be specific to the drug industry, where they are (maybe) useful, and wouldn't distort other industries where patents are actively harmful.

If you get your drug approved by the FDA, you get 5 years of market exclusivity (12 years of it's a biologic). However, it has to be determined by the FDA to be a NCE (new chemical entity). Right now, a company called Amarin is trying to get a drug approved that has no patent and they are hope to get the FDA to recognize their drug as an NCE.

If it for a very rare disease (orphan drug), you get 7 years of exclusivity (still 12 if it's a biologic).

During that time, no other application for the same NCE and indication will be approved by the FDA, giving the first applicant de facto market exclusivity in lieu of a actual patent.