Nintendo recently decided to disallow Let's plays on the platform youtube. As early as 2013, it allegedly already wrote a warning to youtube channels showcasing nintendos content in those vidoes (for those who don't know: Let's play is a form of video format where a person plays through a video game, while giving eigther entertaining, educational, or funny comments), stating that it was infringing copyrights. Unless I am mistaken, legally Let's plays should fall under fair use as "review", since while the Let's player is showing the full game more or less, its his commentary/video feed that actually makes the Let's play. First, nintendo wanted to eigther take down all those videos, or take all the revenue those youtubers are making. Appearently they have now offered a deal for those people, taking "only" 40% of the revenue of all nintendo Let's plays. Now please correct me if Nintendos behaviour is legally correct, but as far as I am aware this should fall under fair use. See https://en.wikipedia.org/wiki/Let's_Play_%28video_gaming%29, under "Legal issues".
You mention that there's some money to be made here, so I'm pretty sure that clouds the legal battle. Again I'm no lawyer, I can't argue if it's legal or illegal in this case.
Second example that I am personally aware of would concern internet movie reviewers like the "Nostalgia Critic", who has received multiple copyright claims and had videos taken down, from big news company TMZ (which he parodied in one of his episodes), and from (relatively unknown) filmmaker "Tommy Wiseau" due to his review of the film "The room". This is the two examples I know of, but appearently those things happened more frequently. Again, correct me if I'm wrong, but aren't movie reviews/parodies supposed to be fair use?
YouTube is not the court. I don't think it's within YouTube's interest to mediate between the two parties. As YouTube, you have companies like Nintendo on one hand who's complaining to you that you are hosting contents that they think are illegal, and you have the other party complaining that it's fair use. What would you do as YouTube? Well, you don't want to show support of one but not the other, so it might as well just take the videos down.
You are free to host the videos, it's just that YouTube doesn't want to be involved in the legal battle. "You two settle this in court, I'm not involved". YouTube taking down videos does not mean it's legal or illegal, it's them washing their hands.