Okay, before I say this: I am NOT a lawyer, but this is my understanding of the situation regarding fair use.
Fair use isn't simply "using short clips", but is also about how short those clips are and how they are used in the context of the other work they are being used in.
In a broad sense, fair use is intended to allow for a number of things, including education, research, review and parody (without it, any negative review of something could be taken down with a copyright strike).
I've seen channels use short, copyrighted clips (generally 1-2 seconds long) for comedy. Is this fair use? I don't know. It could be.
Having a video not be monetized would be a count in favor of fair use, but making money off something does not necessarily disqualify it from being fair use.
You see, it's entirely up to a judge to decide whether or not fair use applies in any particular case. This means that there are a lot of cases where things are taken down that SHOULD fall under fair use, but the defendants just don't have the cash to go to court and fight it out.
Personally, I have yet to see a copyright strike because of a super short clip of something. Buuuuuuuut, I shy away from using anything copyrighted in my videos.
Then again, I know for a fact that I'm kind of on the paranoid side when it comes to copyright, so yeah.
Source: I did a ridiculous amount of research on this a few years ago when I was setting up a gaming channel. It was all from Google searches and Wikipedia.