Right now, investment in infrastructure needs to be made to move power from Manapōuri to the North Island.
As to why we are not replacing the 1.8m tons of coal we import from as far away as Indonesia with wind or solar in the North Island? I don't know.
Edit: If you take a look here, as of an hour ago we are generating 90+% renewable, but with 192mw of coal generation. Wind is generating at a fraction of capacity and this probably accounts for the coal.
There is hydro capacity but that might be from dams far south.
https://www.transpower.co.nz/system-operator/live-system-and...
Why not install 7 more? That would allow the entire current demand for the entire of NZ to come from the south island.
10M USD per km, average 800km from centre of south island to Auckland, $8b in total. 43,000 GWh generation per years, that's just 2.5c per kWh over 10 years on your bill.
https://www.researchgate.net/figure/Indicative-capital-cost-...
Unless there were plans for major new hydro schemes in the South Island there's no particular reason not to just build new generation in the North. There is ample wind and geothermal in the North Island.
This would all change if the Tiwai Pt aluminium smelter were to close as that would leave a huge amount of generation that would need to go north to be used.
There is a very high bar for building infrastructure accross the Cook Strait due to environmental concerns.
The problem is a lot of our power is far south, not center of the South Island, and our costs to build are likely multiples of what is costs overseas.