It's not as reasonable as it gets. Plenty of other companies are ecstatic with the free publicity of gameplay videos and do not attempt to take any of the ad revenue. That's why it was seen as ridiculous that Nintendo took the stance that it did.
By modern standards Nintendo is an odd duck. Some of the things they do is outright antiquated (and I don't mean just videos) and some of the other things they do are weird. With that said, Nintendo markets differently and their customer base is wider than just "core gamers", so what works for the latter isn't necessarily the right move for Nintendo.
Since starting with Nintendo Directs, Nintendo has started doing a lot of low-key publicity on their own. The Directs are chock-full of gameplay footage (especially near launch time) and Nintendo frequently posts additional gameplay videos. Furthermore Nintendo seeds the press with review copies of games weeks in advance, and lets those reviews be published well before a game actually launches. This means that those reviewers have also put out their gameplay videos well in advance, and have had plenty of time to put them together.
This is massively different from how many other publishers handle promotions, as Nintendo is far more "open" than most publishers. Take the just-launched Watch Dogs for example: not only did Ubisoft primarily focus on cinematic trailers, but they gave reviewers a relatively short amount of time to work on their reviews and didn't allow reviews to be published until after the game shipped. I'd prefer not to be cynical, but when Ubisoft says that it's their most pre-ordered game yet, it's not a big leap to suspect that they are withholding information because it would hurt sales. Which makes reviews and gameplay videos all the more important, as this information isn't otherwise being volunteered in a timely manner.
The point of this being that while the "free publicity" angle can definitely help companies and buyers, the games that benefit the most are the games where the publisher is "closed" and withhold information, followed by indie games where they just outright lack promotion. Nintendo doesn't fall in to either of these categories; they have plenty of promotion and they demonstrate gameplay in a relatively transparent and open manner. Which is not to say that Nintendo should discourage these videos, but it's hard to imagine they gain much from them.