That's what we did in undergraduate. Practically every class I had required a research paper. We didn't always have to use statistics, but we were graded on methodology. Recall exams were rare, most exams involved interpretation and explanation. Of course I studied political science, things may be different in other fields.
Perhaps rather than placing so much emphasis on memorization recall exams, undergraduate evaluation should be based on exercising the research and peer review process. The best way to learn research is to do research.