Can’t speak for part 23 directly, but the text (intent) appears similar to part 25.
Whilst there have been standardisation efforts in the determination of landing distance tests, the steep approach requirements originated from a FAA category “STOL” (circa 1980) which applied primarily to operations with specialist aircraft.
The essence of the STOL advice was incorporated in a certification working paper used primarily by the Canadians (DHC) and then the UK (special conditions) before this document was incorporated in JAR-OPS and CS25 (circa 1995). Harmonisation with the FAA turns full circle to part 25.
The steep approach requirements allows the use of 35ft screen height vice 50ft for approaches above 4.5 deg, but is was judged that part 25 aircraft required more precise ‘external’ vertical guidance (collision risk / obstacle clearance), hence the need for a precision glideslope - electronic ILS/MLS or if visual PAPI or similar. IIRC neither GPS nor VASI are acceptable.
Thus aircraft used for commercial operations require an external glideslope and instrument display, particularly so in the confines of the quoted regulation – ‘landing distance’; but perhaps GA operations no so.
Part 25 steep approach has other airborne performance demonstrations and handling requirements.
Some aircraft are able to claim landing distance credit from the geometric advantage of a low screen height and a corresponding low flare height, also that if manufacturers had demonstrated ‘3 deg performance’ from a steeper approach, then these actual distances could offset some of the additional margin requirements.