It seems very airport dependent.
BNE always want the plastic bag when checkin in with other luggage (and then deposit at oversized baggage), most other airports not interested in a bag, and some let you just put it on the conveyor belt with the rest of your luggage.
There's also huge variability in which QF ports you can gate-check the collapsible stroller and which ones you can't.
Virgin are far more consistent in gate-checking being allowed (almost everywhere IME).