To be totally honest with you, it would appear like they're destroying an organically grown facet of gaming culture in the foot. And so what if people make money doing Let's Plays? More power to them. I rarely watch LP's myself, and even then the few LP's I do watch tend to be totally non-profit, but if someone is providing you with entertainment, I don't see why they don't deserve to make some money doing so. A lot of us give these LP's money to enable them to continue doing this, myself included, because it is entertaining and they deserve money for entertaining us.
Think of it in a similar way to musicians, while LP's aren't really artistic expression in the same way that music is, there's a difference between people who do stuff on the cheap in their bedrooms for fun vs people who actually put the effort in to put out something that is polished and professional, and when someone goes the extra mile to provide you with something that IS of a professional level of quality, I don't think it's at all wrong that they get paid for their work a bit.
Nintendo are totally within their rights to enforce copyright claims with LP-ers, but just because they can doesn't mean they should. LP is a legitimate part of gaming culture, for better or for worse and there are indeed people who work their butts off to provide quality content. In doing this Nintendo is screwing people out of a livelihood (or a hobby) that they have the right to. What's next, are we going to start firing games reviewers? Their livelihood is also based around playing games and talking about them, it's a different format but it's not really any different. We accept that reviews are a niche in the market that has been filled, and there's clearly a demand for LP videos, otherwise people wouldn't watch them.
I do miss the days when we actually purchased products rather than simply renting them.