And yet, for Russia to keep it, Russia only has to do absolutely nothing. Russia has no more reason to leave Alaska than to leave any other part of the Arctic.
I'm rather more annoyed by the idea that any random up and comer can (and will have the intention to) buy Alaska, and always around the same time if not the same year. Granted, it wasn't seriously discussed but I remember at least a Mexican Alaska, a Confederate Alaska and a couple of WIs about a Japanese Alaska.
Japanese Alaska doesn't seem unreasonable, although it would require some definite changes pre 17th Century or late 19th Century. Mexican and Confederate Alaska seem more of a stretch to me actually.
For the Russians to keep they do have to do something. They have to keep spending money to support their presence in Alaska, one that has to import its food and every other necessity from the Americans or Canadians, or a massive logistical effort in terms of distance across Siberia or via an extraordinary (in terms of time) voyage from St Petersburg.
With the risk that the British might decide to take it at some point too....
So selling it was worthwhile from that standpoint.