Denti,
I dug into this a bit, as ANP growth is always a consideration in RNP design.
The INS/IRU is expected to be less than 2nm per 15 minutes. The FTE cannot exceed 1nm for enroute, 0.5 nm for approach transition and missed, and 0.25 nm for a non-precision approach, so one can work backwards to the update timing.
So I guess what you are saying is correct, the RNP approach is good without the GPS update, under some circumstances.
For procedure design, the limiting factor usually being the 0.5nm for the missed, and this is per criteria, not operational use....