The preception is VFR pilots are updating their details so in the event they go missing SAR know where to look. Is this really occurring?
Absolutely, two things happen. Firstly the controller should log the time and your callsign on his/her scratchpad. Secondly, all voice communications are recorded so your diversion is on tape. If anything happens to you and a SAR is required the first thing we'll be asked is 'have you heard from this bloke?' from there they can pull the voice recorded tapes, get the diversion details and start looking for you in the area of your diversion.
Your second point about phraseology: This area is pretty bad, the worst offenders are GA IFR. If you want any pointers on standard phraseology listen to the radio calls from the ML based RFDS, spot on