I think the basic premise is true, Sydney is an expensive place so the ATCS get (I think) 12% more than others for living there. Road traffic is a nightmare and Sydney Airport want their land back.
Airservices also do not think like other ANSPs, who generally put Approach Control next to their towers. This means a Tower might have an Approach Centre half-way up the building, it also aids in cross-training. Western Sydney was probably an option, but I'll bet my boots that Airservices wants to put in a digital (remote) Tower!
Not sure why Perth App is still in Perth given that everything outside 30NM is controlled from Melbourne. CMATS shows most of the QLD RAAF units moving to Brisbane so why not Perth and Pearce to Melbourne?
The British NATS had the same problem with London Approach which was in old RAF hangers north of Heathrow, they moved the facility to a new ATC Centre at Swanwick, near Southampton, a beautiful part of England. Once all of the problems with housing, schools, partners jobs and so on were fixed, I am sure the controllers are much happier.