Why do you think this would be billions? The track is already there, though probably not enough is double tracked so over time that would have to be done, but the proposal is really just reinstating the passenger network that was slowly downgraded & then eventually cancelled from the early 50s to the mid 70s.

https://en.wikipedia.org/wiki/Rail_transport_in_Christchurch

There were a lot of stations, and i'd wager most of these the land & surrounds are still in Kiwirail's ownership, they may only be platforms now or not even that but looking at satellite imagery some still exist.

https://en.wikipedia.org/wiki/List_of_Christchurch_railway_stations

Christchurch's rail network is probably more extensive than people think, because it is where the Main North & Main South lines join and the latter goes all the way through to Lyttleton. Its almost exclusively freight of course but the rails are all still there & are still being used.

So you're looking at a new operational company to setup, some DE units, staff and then access rights to coordinate with freight & the other passenger services and building platforms; the latter don't need to be fancy - most of Wellington's are just concrete at the level of the carriage and a couple of shelters.

Its the same reason its not ludicrous to suggest passenger rail in Hawkes Bay as well - even though there hasn't been passenger trains for a couple of decades most of the old stuff is still there in some form - and most importantly is still part of the rail corridor. You just need car parking, bike racks and some larger-than-bus shelters and then figure out a vehicle type you can run frequently enough with low enough staff costs.