you could not trust aircraft to stick to the SID/STAR centerline
In purely technical (avionics) terms, I cannot understand that.
Both DME/DME corrected INS, and GPS, are capable of keeping you (on autopilot) within a few tens of metres of the programmed track.
PRNAV does not in the slightest way affect lateral navigation accuracy.
Is this some ATC-procedural thing? Or perhaps you had airliners which were flying non-RNAV sids/stars using some old FMS which used VOR/DME as the nav source?