The Lakeland approach you show does not have a FAF (Final Approach Fix) because there is no defined point (fix), where you are established inbound and start to descend. In this case, the FAF is given by the FAP (Final Approach Point):
FINAL APPROACH POINT− The point, applicable
only to a nonprecision approach with no depicted
FAF (such as an on airport VOR),...
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 ...
I have some trouble understanding how the procedure designers take into consideration the traffic flow from neighboring arrival procedures
We only concern ourselves with terrain and obstacle clearance. Doc 8168 Vol. II I-2-1-1 refers.
Deconfliction is an ATM responsibility, covered in Doc 4444.
[Modifying per Michael Hall's comments]
If the question is "do you have to fly the full distance indicated in the hold?", the answer is no. (But if it's just about timing vs. distance then ¯_(ツ)_/¯.)
I realize this is old, but since it's currently the top hit on google for the question "do you have to fly the distance shown on a depicted hold&...