I've seen LLZ intercepts from 90 degrees to the LLZ and at ranges from 10 down to 5 nm from touchdown, even in very poor weather. I've seen aircraft whistle through the LLZ and (eventually) correct and some which clearly capture the GP from above.
No! Radar is 'history' in terms of displayed height and ground speed - we have (naturally) a much greater dynamic picture of the state of the aircraft, in terms of airspeed trends, actual wind readings, and a far better appreciation of the time and distance required to configure the aeroplane and correct back to datums from any deviation.
The one thing to remember is if the aircraft has been cleared for a self-positioned ILS direct to the FAF, unless it's following a State published procedure that facilitates this type of approach, in a radar environment ~ certainly in the UK ~ ATC retains the responsibility for terrain clearance and also a responsibility to instruct the aircraft to either break off the approach (or to go-around if inside the FAF) if it appears 'dangerously positioned'.
Agreed that being 'dangerously positioned' more usually relates to a lateral deviation from the FAT, but it certainly would also apply if the aircraft was observed to be 'significantly' below the glide-path.
