This is actually a really good INITIAL thread idea and I would like to continue the discussion because I have thought about this myself many times.
Sony and Microsoft were in much better positions to oust Nintendo, and unfortunately they didn't take advantage of it while they could. Nintendo were flailing, while still making profit, they were dropping slowly and couldn't maintain that during the GameCube days.
This is where I come to start thinking about the difference in direction and the difference in goals from each of the companies... Nintendo does extremely well to stay in the market like this. Sony and Microsoft both seem to bleed money in their gaming divisions yet Nintendo only has their gaming division to make money from. I think it's admirable that Nintendo continue to make money in a market that Sony and Microsoft struggle so hard to make money in.
That said, is it really fair for Nintendo to have to compete with these two behemoths? Nintendo would have ran over Microsoft with a freight truck if Microsoft only had their gaming division, but that really means nothing.
Should this be something that Nintendo may seek to do? Move their operations to another form of media and entertainment? Can they innovate on a different front for consumers? Who knows but I wouldn't want to be the CEO of Nintendo that's for sure, Iwata is a good man!