The origin of the difference between polar and equatorial latitudes has to do with the magnetic field deflecting charged particles moving perpendicular to the field but leaving them unaffected if they move parallel to the field. The Earth's magnetic field is close to vertical at polar latitudes and thus will allow charged particles to reach aviation altitudes more easily.

One thing to note is that when talking about being close to the pole, the relevant pole is the magnetic pole, located in the vicinity of northwestern Greenland, rather than the geographic pole. Great circles for flights from northern Europe to the US west coast and from almost anywhere in Europe to Anchorage come just as close to the magnetic pole as flights from the US east coast to Japan. So, whether or not this is a serious health risk it's certainly not a new one that has appeared just because of the recently opened polar flights.