Why do the RNAV (GPS) approaches to KAPC not use the same missed approach procedure as the ILS/LOC approach?
As best I can understand from the TERPS, it's because there are certain criteria for RNAV missed approaches that wouldn't be met by copying the ILS missed approach.

Specifically, I found the following (see chapters 7 and 15):


In RNAV missed approaches "turns shall not exceed 120°", but the ILS missed approach requires about a 180° turn. There's some related information here about the FAA testing turns greater than 120° in RNAV instrument procedures, it looks like some avionics can't handle them properly.
RNAV missed approaches are made up of legs between waypoints, and the first leg after the MAP has a required minimum length "to allow the aircraft's stabilization on course immediately after the MAP". Unfortunately I couldn't identify what that length is, because the FAA's PDF quality is abysmal and some information is unreadable, but the ILS missed approach requires a turn after a climb of less than 300' (from 214' to 500'), so the distance traveled in that time would presumably be quite small. If the RNAV minimum leg length is significantly greater than that distance, then it might be necessary to continue straight ahead, as both RNAV approaches do.


I'm certainly not a TERPS expert and there may well be other reasons for not using the ILS missed approach, but those two points seem to show that the criteria for designing missed approaches is different enough between procedure types that you can't just 're-use' them freely.