I believe
2 sheds reply is the best explanation.
The purpose of the report is to signify the point of termination of radar vectoring by ATC to a pilot interpreted final approach and reestablishment of pilot navigation.
If you have flown the entire procedure under pilot navigation then there is no reason to report established, although many controllers will request it.
kenparry I'm not sure if your quote is verbatum from Cap 413 but if so, I find the sequence of instruction ambiguous.
BIGJET 347, cleared straight in ILS
approach runway 28, descend to altitude 3000 feet
Surely the last altitude instruction would override the clearance for final? Assuming the ILS commences at 3000 ft, I think the instuction should read, "Descend to altitude 3000 feet, cleared straight in ILS approach runway 28. "(By the way, if the angle of intercept is within 30 degs, I believe the "straight in" bit is redundant")