Even if Nintendo is held in such high regard by the public, they often choose a different path than what's considered to be mainstream. In fact, when it comes to streaming services such as the popular Twitch, Nintendo doesn't want any part of it - at least when it comes to streaming gameplay.
Both Microsoft and Sony have had success with offering this service to their players, and it's also proven to be a good way for publishers to show off their games. Nintendo, on the other hand, is not going to provide the same service anywhere in the near future.
Polygon spoke with Nintendo of America president Reginald Fils-Aime about this, and he said "We don't think streaming 30 minutes of gameplay by itself is a lot of fun", and by that he meant that streaming gameplay through Twitch does not fit Nintendo's philosophy which states that all of their content has to be fun.