I suppose the idea of being allowed drive unsupervised on Prov. 2is that by that stage you have 2 years experience. You do not need to sit a test as far as I know for Prov 2. However to get Prov 3 you need to sit the test. The warped logic is i suppose is if you are on your third or more provisional you have failed your test and need supervision
You don't necessarily have 2 years experience by the time your first provisional licence has expired. When I got my first licence I rarely sat behind the wheel and had practically no experience by the time it expired. I was then, theoretically entitled to drive alone for 2 years.