There is a long term 3.2 RNAV trial going on, and there have been trials of steeper segmented glide slopes (4.0 degrees then changing to 3.0 degrees at 4DME, that type of thing) as well.

There are a few problems.

Once you get above 3.2 then CAT III approaches are not going to be flown (that’s the certification limit for most airliners (well, 3.25)).

Once you get above 3.5 degrees then energy and speed management become very critical, so the chances of aircraft being able to maintain an ATC-specified speed down final approach with minimum separation both ahead and behind become slim to non-existent. On some of the vertical segmented trials, 777s had to be flying at 160kts at 25nm from touchdown joining the 4.0 degree slope to ensure they were still flying 160kts at 4DME and able to slow to finally approach speed. Modern airliners are so efficient in terms of drag that they are difficult enough to slow down without hanging everything down which actually makes them a lot more noisy than a cleaner aircraft on a 3 degree slope.

Because of the difficulties discussed above, steep approaches greater than 4 deg (last time I looked at regs) require that the aircraft be specifically certificated for these operations. Basically to show manoeuvre margin and flare / GA handling. The ability to manoeuvre is directly related to drag - slow down, minimum thrust - air bleed / elect gen.
Actual operations encounter further difficulties, as above, particularly with AWO category, and ATC management.

Steep / two-segment approaches have noise advantages - the main issue at LCY.
Modern aircraft are generally quieter and distant nose is minimised with managed drag etc.

High density airport operations have considered wake turbulence - landing rate advantages when intermixing std / heavy aircraft; those capable of steep approach can land long with separate guidance, but see limits above. Possible ATC implications.

Many new types can achieve category 2, steep approach accuracies. Manual landing in these conditions is ‘disliked’ by the authorities - although the crew have a better view than a standard approach. Autoland is a certification cost issue; Avro RJ had ‘the feel’ of an aircraft which could achieve a steep auto-land - manual landing certificated at 6 deg.

RAE showed steep auto-land capability with HS748 and BAC 1-11 in the 1970s.

I think it’s 4.49 degrees now, the limit before special training and certification is required.