There are 2 seperate issues here. Firstly, in high latitudes in the region of the magnetic pole, the angle of dip and large (and rapidly changing) variations make a magnetic compass unusable. The second is that close to the true N pole, you can't even fly a true heading. Consider flying north along the zero meridian. As you transit the pole, your true heading switches from 360 to 180. Now take a more realistic view as you transit close to the pole on a heading other than north. On a great circle route, your true heading is continually changing, as the pole swings past.
I have flown such a route on a few occasions in a commercial aircraft from New York to Hong Kong. We still fly inertial and GPS great circle track but we display grid north and have a chart with a grid overlay referenced to the Greenwich meridian. So in this case, flying north to the pole along the Greenwich meridian, your true heading is 360 and your grid is 360. As you transit the pole, your grid heading is still 360 but your true is 180!
In days of yore, you synched your DG to the magnetic compass (corrected for variation) on North. After that you plotted each leg on the grid and used grid heading to fly hoping the drift rate was acceptable and you found something you recognized. Much easier with a triple ring-laser gyro inertial and twin GPS! - but no easier to visualize and get your head around........
By the way, the latest Airbuses don't even have a magnetic sensor. They use inertial to get true heading and have a world-wide data-base of the local variation which is applied to display magnetic. Tail wagging the dog, I think. One of my favourite line-check questions - "where is the flux detector on this aircraft?" - gets them every time......