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.