Russian icebreakers have either one or two reactors. The new ones, which will be the largest, heaviest and most powerful icebreakers ever built, will have a thermal output of 2 x 200 MW and propulsion motors rated at 3 x 20 MW. That’s good for about 9’ of solid ice.
While weight (=momentum) helps in certain icebreaking operations, modern icebreakers are no longer the kind of “brute force hammers” they used to be. Operational experience has shown that in a heavy ridge field, it’s better to turn the vessel around and proceed in astern direction. This way, the 980’ by 165’ icebreaking LNG tanker they tested last winter in the Arctic could overtake an Arktika-class nuclear-powered icebreaker which was smaller by beam and displacement, and had slightly more propulsion power, but could only operate in the traditional “ramming and backing” mode.
Your note about the beam of the icebreaker is of course correct. However, the USCG does not provide “active escort” in the same way as the Russian icebreakers do, so it’s not as critical. However, obviously you can’t make the icebreaker paper-thin; it will still have a much smaller length-to-beam ratio than a typical open water vessel (“short and stubby”). It’s also correct that increasing length does not have a significant impact on straight-line icebreaking performance, but it does reduce the maneuverability of the vessel in ice.