No matter whether some people live on the poles or not, they still live on the earth, the earth revolves around itself every day. I do not think people at the poles are ignorant of that fact or count days following whether the sun sets wholly or not. Do you have any proof that if there is no sunset they don't count a day? Days still exist. Do they count no day at all when it is night for severall calendar days following or it is daytime? Do people at the poles stop sleeiping at night because there is no total darkness or stop waking up because it is dark?
The Qur'an does not disregard common sense, quite the opposite is says rather often to use our reasoning to go through life. Things that are said having in mind humanity will not fit every single person necessarily all the time. We have minds to get the gist of whatever we are told and adapt it. And to do so is perfectly coranic and of the fact that we are reasoning creatures and capable of jusdging matters on common sense is in the knowledge ou our Creator, and it is to us that He addresses itslef, no to some dumb robot which follows ritual commands.
If somebody on the poles wants to benefit from the blessings of ramadan or salat sure it is doable without much mindwringing. If they do not want to, no need either to bring up knowledge or lack of it of the Creator.
I am sure, it is a theoretical problem and not a real one. Just follow their days, they days of the people who live on the poles.