A successful mass transit system almost necessitates being mostly separated from private vehicles; there are plenty of cities around the world that are 500k or smaller which have metro systems so there really isn't much of an excuse for Auckland to not have one.

I think the smallest I can find on a quick google today is Lausanne which is only 150k people but has a separated rubber tired metro of some kind. Ghent is another small one with a mostly separated tram system, Rennes has a mostly underground system and is for an urban area of around 360k.

But we don't even need to look overseas, Wellington Region has 4 1/2 lines for only 550k or so people. 2 of those are fully dedicated to passengers, and one of the others is almost entirely passenger as well. Mixed Freight & Passenger works in NZ, we've been doing it for decades.