Diesel electrics can only operate under ice as long as their batteries last, that's probably why they don't go there. Nuke's have no such limitations. The Swedes have a class of subs powered by Stirling Engines that can stay submerged for weeks. They are also super quiet. During an exercise off San Diego, one of them penetrated a US carrier group and could have sunk the carrier.
https://en.wikipedia.org/wiki/Gotland-class_submarine