Yep, people have that right to upload and monetize but it doesn't mean they should or should be able to get away with it. They can still get those videos flagged down or monetized by other IP owners who also have rights.
No, the people do not have the right to upload and monetize the videos unless they have been specifically granted them from the owner/ creator... who are the only people who do have any rights in regards to this.
However, you seem to be a legal expert when it comes copyright with gameplay and reaction videos on YouTube so I'd like to hear more about your insights into fair use with regards to gameplay content which is copyrighted.
I would not consider myself an expert, just someone who has been around for long enough.
Game play content is only allowed when granted the rights by the game developer/ distributor. Some do and there are no problems, some don't and problems arise. Once again though, game play videos have virtually nothing to do with (or in common) with reaction videos. I'm not sure what your hang-up is on this, but they are not the same.
Because if reaction videos are not in fact truly commentary or analysis and do not meet the four criteria for fair use than neither does lets plays and most other gameplay type videos which is why Game Developers can renege on their policies towards Gameplay channels at any moment and hit them with copyright strikes for monetary gain without any notice. Same thing applies to content owners who have their content reacted to on such channels. Some creators are okay with having their content reacted to and monetized on other channels and some are not. Some Game Developers and Publishers are fine with having their copyrighted material uploaded and monetized and some aren't.
And, once again, they are not comparable. At the very least, it is often in the terms of agreement of using a game of how video from a game can or can not be used.
As for how most reaction videos should not be allowed is simple... there are 4 keys used in determining whether something is used under fair use or if it violates copyright. In regards to reaction videos, the first (if it advances knowledge or the progress of the arts through the addition of something new) would be somewhat of a grey area, but the 3rd and 4th keys are fairly obvious violations.
The third key questions how much original content was used (the less the better) and how much of "heart of" the original was used. Since the majority of reaction videos show the original video in its entirety or, at the very least, its most important parts, it's a fairly clear violation of this test.
The 4th factor is if the diminishes the value of the original work. Since most reaction videos show the original work with a smaller thumbnail of whoever is said to be reacting to it, it is clearly competing against the original work. After all, having watched a reaction video showing the original in its entirety, there's little to no need to watch the original posting.