I agree with Oldebloke. Alot of airports have FAF that start below 2000' and generally ATC will clear you to that altitude. If you choose to descent on a 3deg profile you will capture the ILS earlier so do remember the Height cross-check when captured. It is perfectly legal.
The approach chart caters for a LLZ (for alt-dme checks) as well as being noise sensitive (ie KIX FAF is at 1200' and there are height crossing restrictions) and of course obstacle clearance.
But i am not sure if beam strength has anything to do with it...stronger as you get closer?? or just more sensitive!!
HSD