Air NZ has only rebooked me on alternative carriers as Elite - cancellations prior were done that way. Generally agree there is no reason why they didn't do it, but airport staff are usually pretty hopeless/tied when i tomces to rebookings as it is all managed via call center.
It pains me to read that you missed the flight by a few minutes as I've had travelling companions where staff made exceptions after gate is closed for TT (by a lot of convincing). From my expereince , I avoid the bus and opt of a quick sprint which could have saved minutes.