According to the Jeppesen Manual, noise abatement section for YSSY, there is no requirement for an ICAO 'A' departure from any of the runways if your aircraft has engines with a by-pass ratio of 3.5 or better.
(Jeppesen YSSY page 10.4A)
QANTAS, and maybe other airlines choose to fly an ICAO 'A' but it is not required. That's why some airlines are fast and clean and others are not.
On further investigation I just noticed this para in the Aussie AIP Noise Abatement Section for YSSY.
Page 1
Para 1.2 Jet noise abatement climb procedures apply for the following runways,
Runway 16R 2300-6000 HR local time.
Runways 34L & 34R at other times.
So according to the local rulebook it is required.
Regards,
BH.