Re: “… after all, the autopilot will fly the GP whatever angle it is”. (#3)
Not necessarily so. Some auto-flight systems might schedule glideslope control gains with altitude or configuration, which could alter the relationship between alt/range or time-duration on steeper approaches. Also a steeper glideslope beam may have a different sensitivity than that at 3deg – constant beam width at higher angle has a different vertical spread. Don’t forget other systems e.g. EGPWS.
The aircraft certification (for GS > 4.5 deg) may require a specific configuration or procedure, but most aircraft should be able to fly 3.5 deg without systems modification.
The BAe146/Avro RJ AFM has a chart of noise benefit against approach angle. These aircraft demonstrated Cat 2 tracking accuracy at LCY as part of their certification (LCY GS is Cat 2 equivalent), but the authorities mistakenly insisted on greater visibility requirements, even though a steeper approach provides a better over-the-nose view.
LCY has always been a constant angle approach.
RAE trials (1970s) demonstrated two segment approaches and autolands to Cat 3 standards for BAc1-11 sized aircraft and considered the feasibility for larger types such as the Tristar. A 6 deg to 3 deg changeover required a corner point at approx 1000ft (2nm @ 6 deg) to enable the final approach to be sufficiently stable.
MLS trials demonstrated two-stage segmented and offset (curved path) approaches which have additional noise reduction benefits. Some work was also done on intermixing normal approaches with steep approach capable aircraft, which used an alternative GS beam to land further into the runway with significant noise benefit and increased traffic landing rates due to wake turbulence avoidance.