Here's the thing: Nintendo has the legal right to prosecute everyone and anyone that uses their IP without their permission. This can range from someone using a Nintendo character on their bakery shop to a videogame publishing company including Mario in one of their titles without Nintendo's permission.
And then the issue of copyright:
I mean, even using a profile image with a Nintendo character is copyright infringement, and so is uploading gameplay videos under most circumstances, even if youtubers insert a "fair use" notice at the beginning of the video. Sharing memes that feature Nintendo characters is also copyright infringement. Nintendo could very well strike these down. There'd outrage, but they're within their legal right to remove from the internet (or any other medium) any unauthorized reproductions of their IP. They're protecting it from "pirates", after all. The first Super Mario game was released in 1985, which means it'll enter the public domain in 2080, and that's assuming the Congress of the US doesn't approve any more retroactive copyright extensions. That's insanity.
This isn't a problem with Nintendo, this is a problem with copyright.