I think you have it right after all the posts! The reason to cut the roots is to:
1) get better access to the ball itself to clean out old roots and old media,
2) preclude more breakage,
3) keep the roots off the bottom of the pot (final trim may be necessary to catch the few long ones.) Although roots eventually grow to the bottom, placing freshly cut ones on the bottom, generally sitting in more moisture, tend to cause rot.
4) fill the pot with mix, not a bunch of broken roots which will not absorb water but die and rot instead.
Thanks Rosie for the words of support. Nothing better than a successful student to make a teacher look good