Why is this Instrument Approach NA for certain radials, yet it depicts a feeder route for those radials?
Your confusion may stem from the way you are viewing the instruction not to use it for arrival on the radials 356 to 157. If you were arriving on the 356 Radial of the PIE VORTAC, your course/track (and/or heading in calm winds) would be 176°. If you were arriving on the 157 Radial of the PIE VORTAC, your course/track (and/or heading in calm winds) would be 337°. If you were arriving on the 85 Radial of the PIE VORTAC, your course/track (and/or heading in calm winds) would be 265°. All of these arrivals would necessitate a hard, sharp turn at a potentially steep bank angle. This will need to be avoided.
You are able to use other routes to the Initial Approach Fix other than flying first to the PIE VORTAC. Like flying directly to the RUYKI waypoint as your first point on the IAP. This is especially valid since arriving on any of the above mentioned courses/tracks will place RUYKI in easy access of the pilot. This would be much simpler than trying to make that hard, sharp turn at a steep bank angle. Only minor adjustments from the arrival course/track at an appropriate distance from RUYKI would need to be made. This has the added benefit of reducing confusion and freeing up airspace from conflicting traffic.
If you are concerned with using the STARs as feeder routes, you would use the PIE VORTAC as your transition to the IAP from all STARs with endpoints West of KTAP. You would fly directly to RUYKI from all STARs with endpoints East of the IAP. If you have to lose altitude from your descent from the STARs, you would use the Hold en lieu of a course reversal to do so.