Some units have incorporated the "further with the glide path" (TC for one) into their local MATS Part 2. However, that as well is an abridged version of the correct phraseology.
"......when established on the localiser, further descent with the glide path" is used, especially during a busy sequence, and eliminates the situation of a pilot waiting, waiting, waiting to get in on the r/t to confirm they can descend further. The reason, take EGLL for example. Especially on 27, with the helicopter routes over the city, if an a/c is descending on the glide path, it is separated from the standard alititudes on the routes. Also, as our usual descent is to 4000' (as EGLC uses 3000' below us), once again, if established and descend on the G.P., the descent from 4000' at about 12 miles is also separated.
As an aside for a point of discussion, why is there the requirement for the good old "turn left heading ..., REPORT localiser established Rwy ...". I'm looking at the radar, I can see if they have established or gone through. I have never really seen the point. What's wrong with "turn left to intercept localiser Rwy..."? And I'm with Flower with the "range from touchdown" issue for straight in/on the ILS. If the driver can't get a DME range, they'll tell you and ask for it (we'll not go into the closing the localiser from the left/right!)