I fly over the ditch to MEL few times a year, OOL at least once a year and occasionally to SYD, and never had issues with priority baggage handling with NZ/VA. Always have Star Alliance or VA tags on properly at check-in and bags almost always there waiting for me, or less than 5-10 minutes wait at most once I clear immigration.

In fact I'd say my bags being >20 mins wait is the exception to the norm (once every 6-7 flights at most?)

Perhaps its something QF or OW in general just lacks discipline?