The biggest problem for this proposal is the current state of the rail line to Northland. However all relocation proposals to some extent especially an alternative, the Firth of Thames, are affected to some degree. (Firth of Thames is better than the alternative Manukau because it is on the same side of the country as Tauranga)
Basically the Northland line would have to be doubled which includes all the bridges and tunnels unless these are left as single track sections, but this increases the costs of signalling all the transitions from single to double track. How Tauranga wins at present in competition with Port of Auckland for freight in the Auckland region is that the Auckland to Hamilton line except for a short section through the Whangamarino Swamp is all double tracked and has been for 50 years.
I have no idea of the claims that it will cost this amount or that amount. The new Marsden Point line that is proposed will be another cost.
Essentially this proposal is like suggesting we should close down Port of Lyttelton in the South Island in favour of Picton. There is a rail network but it makes no sense to move the large volumes of freight the extra distance by rail unless there is zero alternative. I don't think the arguments about Northland being closer to shipping lanes matter that much. It is still cheaper to keep the freight on the ship and unload at Auckland than moving it by rail because the rail line would have to be engineered for extremely large and heavy trains to be able to compete with the large container ships that will be coming to NZ in the future.
Port of Tauranga can already compete effectively with Auckland without needing more money spent on rail line upgrades (OK, they have had some financed already by Kiwirail which means taxpayers probably contributed to it) and coastal shipping to Northland from Auckland is a viable alternative to rail that doesn't require the expenditure on the tracks. It's almost totally guaranteed that if Northport takes a lot of the existing Auckland freight that large amounts of that freight will go by road. Because for example to move the vehicles you will need to equip special trains with special wagons that don't exist now, which is all a waste of time and money when all that is needed is for the ship they are being transported on to go to a different port. Rail falls down when special wagons have to be purchased for a particular traffic. It is true that you do need special car transporter trucks but there would be companies building them in NZ whereas rail wagons would probably have to be built overseas and shipped to here.
Some political parties have got sensible approaches to coastal shipping as an alternative to rail, because our population distribution is mainly near ports (Hamilton and Palmerston North being among the few exceptions) meaning coastal shipping is viable and even the likes of Mainfreight are saying they want to keep it as an option on the Lyttelton-Wellington run. It has to be remembered Mainfreight got their start by using coastal shipping to undermine what was then the NZR rail network. Fast forward and Kiwirail still has a monopoly, but only on rail itself.