Notimtams
All the instrument approaches in to YBAF cross CTA, including the missed approaches.
If you have done a few, I am sure you have noticed that you are in the same bit of airspace as the landing aircraft 01 in to Brisbane, and have to be practically included in the sequence.
So, your basic answer as to why....it's where they put the damn airport! (BN RWY 01 IAF)
The procedure we use has a lot of legalese included in it, because radar lowest safe altitudes are being used that are sometimes in and sometimes out of controlleed airspace.
I have often argued for a 'corridor' aligned with the approaches/departure tracks for AF that is class G to allow no requirments for ATC to get involved when AF TWR go home at 1800. The process to achieve that is beyond mere mortals like me.
FYI our lowest assignable level in the AF CTR is 1900' - so that is generally why an aircraft leaving CTA for AF CTAF(R) is going to remain in CTA until established in the circling area and (reported) left/main 1500 or left 1500 in the IAL - a lot of frequency juggling and workload as you say.
BTW the only instrument aproach that does not require ATC involvement is the 28RNAV, as all the NDB APCH are RADAR-NDB's.