There seem to be two different things being discussed here - RNAV arrivals (i.e. STARS) and RNAV approaches.
Under the Canadian system, an RNAV arrival can certainly cut down on RT. If there's no traffic or the aircraft happens to fit into a sequence nicely, just clear it for the approach on first contact, or via an intermediate waypoint if there's an operational advantage to doing so. An open RNAV arrival terminates at the "downwind termination waypoint", and if they haven't got an approach clearance by 3 NM before it they just continue downwind, nice and orderly. A closed RNAV arrival (or straight-in) terminates at the FACF and that can be a hassle, as virtually any traffic nearby will lead to the termination of the arrival and out come the vectors. Usually, an RNAV arrival will be followed by a precision or instrument approach just as with vectors or a conventional STAR.
An RNAV approach is a different kettle of fish. They still have to get to the FACF to commence it so there's no reduction in RT unless it's preceded by an RNAV STAR. The real problem is missed approaches, at least in Canada. One company has its own, company-specific RNAV approaches approved by Transport Canada, but the missed approaches bare no resemblance to those for ILS or NDB approaches, and in one case goes into Class F advisory airspace where ATC cannot take IFR aircraft.