I think all of the complaints with your idea that center around "exam time" being too late would be addressed by sensible quiz policies. i.e. classes should hav

I think all of the complaints with your idea that center around "exam time" being too late would be addressed by sensible quiz policies. i.e. classes should have quizzes frequently, which individually aren't a huge component of the grade, but also which repeatedly cover past material so students can get the benefits of spaced-repetition. The notes correlating phone use can be given on the quizzes. The only issue I have with your idea in spirit is that it does nothing for the other innocent students who get distracted by the people goofing off on their phones, but this might just be addressed by cracking down on distracting use but if people want to quietly text or browse the web under the desk for the whole period that's their business / responsibility come quiz/exam time.