Wow, I am a bit lost here. My 2 cents worth (which will probably be off the mark) is as follows:
-ATC clears you for a particular STAR before TOPD (generally 99.9% of the time)
-On the way down you report 'visual' (i.e requesting a visual approach)
-ATC clears you for a visual approach
You must continue to follow the STAR until within 5nm (day) or circling area/5nm on VASIS/10nm ILS etc (Night) but can descend at your discretion provided you maintain 500' above CTA and above MSA (night)
So essentially, the purpose really is to remove the vertical responsibility from ATC. THe clearance authorised by ATC is the STAR so that becomes the lateral tracking requirement.
Of course, if you request direct to a 5nm final and request a visual approach then that is a different story.