A political issue with this is that Northern Norway has been exempt from the 25% VAT as one of many measures to make living in Northern Norway more attractive. Until now the cost of power in both north and south has been pretty much the same, meaning people in power zone NO4 have paid about the same price for power, but not the VAT.
But now that the price has gone up by such an enormous amount in the south, connecting north and south will not reduce the price in the other zones, it will likely just cause NO4 to go up to the same level as in the rest of Norway. This is mainly due to the NO4 being basically not connected to the the synchronous grid of Continental Europe, while the other regions are to a much larger extent due to underwater cables going to the UK, Denmark and Germany. This means that the price of power in Europe directly influences the price of electricity in NO1-3, but not NO4. At least not to the same extent, although Sweden makes a killing buying cheap power from NO4 and selling it to mainland Europe, or even straight back to southern Norway. As such, connecting NO4 to the rest of Norway and by extention the European grid, would not be very popular in the north, but to be fair, the price increase has not exactly been popular in the south either.
The industry in Norway is highly electrified and some sectors are very energy intensive, such as aluminium production, which due to using electrolysis, runs almost entirely off the grid. Manufacturing used almost 37% of all power consumed in Norway in 2017, with power-intensive manufacturing accounting for over 80% of total energy use in the manufacturing sector that year.[0] This is also an issue which will need to be considered when talking about increasing transfer capacity between the two zones.
I hope this gives some insight, even if I rambled a bit and touched on a lot of different aspects. I'm by no means an expert, but have become interested in the subject as so many other Norwegians have lately. I'd love to answer more questions if you have any!
[0] https://energifaktanorge.no/en/norsk-energibruk/energibruken... (Source in English and published by the Norwegian Ministry of Petroleum and Energy)