This kind of thing seems to work well enough in Europe.
Right. But you're not in Europe now, Dr @Rikkitic! In Europe they already have intra-city public transport that works. And Europe has a high enough population density (lots of 4-storey apartment blocks) to support it.
This, in big glowing letters,
The Auckland and Waikato regions together are about the same land area as Switzerland, but Switzerland's population is north of 8 million, while Ak+Waikato is just over 2 million.
regional rail in low population areas cane get very expensive very quickly, as this story from Australia shows
It would be cheaper to fly each passenger between Cairns and Brisbane, rather than run the rail, and that's the best performing route...