Other possible causes are
the reverse synchros inside...
When a manual is difficult to get into reverse, it is either due to the reverse lockout failing or
the reverse synchro being worn and taking a few...
Not exact matches
Most cars do not have
synchros on
reverse, so this is a common «problem» (more of a design choice than an actual problem).
This description implies a lack of
synchros, which date back to the 30's, and is not relevant to the question which says nothing about switching between
reverse and forward or grinding specifically at stop lights.
The third - gear
synchro is about shot, and the transmission wants to slot into
reverse only about half the time you try and back up.