15 minutes after what? Landing? Standing at the belt waiting? What's your data source?
15 mins from disembarking, usually takes 5 mins to walk to carousel at SYD and MEL.
My data source in personal experience, flying syd-mel every 2 weeks for years; I fly less now but still go through SYD pretty regularly and have checked luggage about 70% of the time (nothing oversize).
At SYDd I've only waited longer than 20 mins to see luggage start coming out maybe 3 times usually it starts to come out in 15mins. Maybe I've been lucky or maybe it's the times I fly.
Fastest airport by far is ABX, 5 mins max, the beauty of so few flights and small planes.
The worst wait for me at SYDd was almost 2 hours but that was when major weather disruptions saw us land right on curfew, many flights unable to get away, so no free gates, stuck on plane until midnight then luggage at 2am. But most of the handlers shift would have ended well before we got to the gate. It was cough but far from the norm. The other two times, also during weather disruptions circa 30--35mins.
SYD International rarely quicker than 30mins, often 45mins, once it took an hour, but I was talking domestic.
It's certainly not the former in my experience domestically in Australia. At PER QF domestic you're lucky if the belt has even started moving 30 minutes post landing. Also, they can't do priority bags either.
Priority bags work maybe 50% of time. I find if check in really early less likely priority works. Only been through PER a handful of times, don't recall waiting too long but then again they don't call WA wait a while for nothing.