Yes, better investment in public transport would be great. It reduces congestion on roads at peak times, which I think people forget when arguing roads need the funding.
However, I'll propose an alternative us of some of that money. Over the past decade or more, trucks have got larger and heavier. How many trucks are driving Wellington to Auckland or back each day?
Have we got data on the reduction in road damage if we could divert half those trucks onto rail, with a rail hub at each end for the deliveries to final destination?
For 46 billion, we could probably do a couple of rail hubs, a massive investment in public transport, and have some money left over for a few roads that are in dire straits.