I personally feel that it's a bad idea. Doing so would produce parts with lower quality than other parts. For the case of places that need to be divided into thirds, I think they need to be dealt with on a case-by-case basis. They can already use 48 primitives, but where that's overkill, Philo's point that p/12 in theory already works is valid (as would be p/18 and p/24).
Having said all that, I'm not a parts author, so please take my input with a grain of salt.
Having said all that, I'm not a parts author, so please take my input with a grain of salt.