I was quite surprised by your claim, as I'm quite sure it is a right in EU and other countries. It seems you have been correct, though not any more. See quote[1]:
The U.S. Supreme Court has traditionally characterized fair use as an affirmative defense, but in .. (2015) .. U.S. Court of Appeals .. concluded that fair use was not merely a defense .. but was an expressly authorized right, and an exception to the exclusive rights granted to the author of a creative work by copyright law.
Fair use is still a defense to copyright violations, not a right. The 9th Circuit did not hold that fair use was a right in that case (the dancing baby case), only that a copyright holder must consider whether the alleged violation was potentially fair use before filing a lawsuit.
Importantly, the copyright holder is only required to consider whether the violation is fair use. They can still decide that it is not, and proceed with their lawsuit, with the only additional effort required being to state in their claim that they considered fair use and decided that the violation was not fair use.
(Note: while the 9th Circuit precedent is limited to the West Coast of the US, because most tech companies are HQ'd in CA or WA, so as a practical matter this case governs the internet.)
I'll quote from the first paragraph of court's opinion:
We hold that the statute requires copyright holders to consider fair use before sending a takedown notification, and that failure to do so raises a triable issue as to whether the copyright holder formed a subjective good faith belief that the use was not authorized by law. [2]
Note that the case was about abuse of DMCA takedowns by copyright holders if not considering fair use. Judge considers fair use as authorized by law, which I would interpret as right, not defense.
Another quote:
We agree with the district court and hold that the statute unambiguously contemplates fair use as a use authorized by the law. [2]
Fair use is not just excused by the law, it is wholly authorized by the law [2]
From previously quoted wikipedia article, the paragraph continues:
"Fair use is therefore distinct from affirmative defenses where a use infringes a copyright, but there is no liability due to a valid excuse, e.g., misuse of a copyright." [1]
As for plaintiff considerations, IMO, of course plaintiff is required to argue it's standing, otherwise the case is thrown out, or in this case DMCA is abused. Normally the first bar is to make a coherent argument, then the court gets to decide whether your opinion is right, but that does not lower the defendant's rights to a "defense", even if they are a defense.
You mostly just restated what I said. The decision merely requires the copyright holder to consider fair use. It doesn't require them to accept that the alleged violation is fair use or even to do a detailed analysis:
In order to comply with the strictures of § 512(c)(3)(A)(v), a copyright holder's consideration of fair use need not be searching or intensive. We follow Rossi's guidance that formation of a subjective good faith belief does not require investigation of the allegedly infringing content
As for the quote, Fair use is not just excused by the law, it is wholly authorized by the law
The court is referring to 17 USC 107. Fair use exists in the context of whether something is a violation of copyright, in the same sense that self-defense is authorized by the law but is still a defense to criminal charges. Notably, I didn't call it an affirmative defense because it is not one.
The U.S. Supreme Court has traditionally characterized fair use as an affirmative defense, but in .. (2015) .. U.S. Court of Appeals .. concluded that fair use was not merely a defense .. but was an expressly authorized right, and an exception to the exclusive rights granted to the author of a creative work by copyright law.
[1] https://en.wikipedia.org/wiki/Fair_use