The claim seems novel, so I looked at several sources, including several recent cases where fair use has been upheld.
In Easter Unlimited Inc v. Rozier, 18-CV-06637 (KAM) (E.D.N.Y. Sep. 27, 2021) the defendant arranged for creation of a cartoon image of himself wearing the copyrighted mask used in the movie Scream. This was found to be fair use, largely on the ground of the transformative nature of the use changing the purpose from evoking horror to a humorous reference to a horrifying movie. Rozier had originally considered using a representation of the hockey mask work by the character Jason in the Friday the 13th series of films.
“Rozier and his management team decided that the clothing line would feature the name “Scary Terry, ” as well as a cartoon drawing of Rozier accompanied by a mask associated with a serial killer from popular horror.” Easter Unlimited, Inc. v. Rozier, 18-CV-06637 (KAM), 42 (E.D.N.Y. Sep. 27, 2021) at page 42
It would seem that the Jason mask would have satisfied the purpose as well as the "Scream" mask. Nothing in the fair use analysis (section C of the opinion, starting at page 31) refereed to a need (to establish fair use) for the work appropriated to serve a legitimate purpose which could not be served without it or any similar concept. This simply was not part of the fair use analysis.
Further the opinion states, at page 17:
“Copyright infringement is a strict liability offense, meaning “intent or knowledge is not an element of infringement.” Fitzgerald Publ'g. Co. v. Baylor Publ'g. Co., 807 F.2d 1110, 1113 (2d Cir. 1986). ” Easter Unlimited, Inc. v. Rozier, 18-CV-06637 (KAM), 17 (E.D.N.Y. Sep. 27, 2021)
This seems to dispose of the de minims exception suggested by supercat's comments cited in the question.
In McGucken v. Pub Ocean Ltd. 2:20-cv-01923-RGK-AS, 2021 U.S. Dist. LEXIS 153361 (C.D. Cal. July 27, 2021) The district court found fair use. The Copyright office's fair use index summarized the case, writing:
Key Facts: Plaintiff Elliot McGucken photographs landscapes and seascapes, which he posts to his public Instagram account. Twelve of McGucken’s Instagram posts depict photographs he took of an ephemeral lake in Death Valley (the “Photographs”). On April 15, 2019, Defendant Pub Ocean Limited (“Pub Ocean”) published McGucken’s Photographs to five websites owned by Pub Ocean as part of an article
written by a freelance writer titled “A Massive Lake Has Just Materialized in the Middle of One of the Hottest Places on Earth.” The article contained ten of the Photographs, with credit to McGucken and a link to his Instagram page, as well as several photos that were not McGucken’s and commentary on the conditions in Death Valley, the Sahara, and other natural phenomenon. McGucken brought an action for copyright infringement and moved for summary judgment, asserting Pub
Ocean’s use did not constitute fair use.
Issue: Whether including photographs posted on social media in a news article to illustrate the subject of the photograph is fair use when accompanied by commentary.
Holding: The court concluded that Pub Ocean’s use of McGucken’s Photographs was fair use. The first factor, the purpose and character of the use, favored fair use because Pub Ocean’s use of the Photographs was transformative because the article included discussion of facts and commentary that provided context for the Photographs and included other photographs as well. The transformative nature of the use reduced
the importance of the commercial purpose factor. The court held the second factor, the nature of the work, disfavored fair use as McGucken’s works, although previously published, are highly creative. The court found the third factor, the amount and substantiality of the work used, favored fair use. The court concluded that, despite displaying the “heart” of the Photographs, the article expressed ideas
“beyond what Plaintiff expressed in his photographs,” rendering the amount of McGucken’s copyrighted images “insubstantial in context.” The fourth factor, the effect of the use upon the potential market for or value of the work, favored fair use because Pub Ocean’s transformative use “mut[ed] the degree of market substitution.” The court also noted that McGucken licensed the Photographs to other publications after Pub Ocean published its article, which indicated that Pub Ocean’s
use did not usurp or destroy the market for the Photographs.
Note that other photos of the same temporary lake would have fulfilled the legitimate purpose of news reporting, and there seems to have been no allegation that these particular images were essential to this purpose, but the court still found fair use.
DMCA Subpoena to YouTube
In In re DMCA Section 512(h) Subpoena to YouTube (Google, Inc.)
United States District Court for the Southern District of New York
January 18, 2022, Decided; January 18, 2022, Filed 7:18-mc-00268 (NSR) the district court considered a motion to quash a subpoena because a claimed infringement was alleged by the defendant to be fair use.
In this case a person using a pseudonym created and posted to YouTube stop-action videos of characters represented by Lego constructions watching and reacting to substantial excerpts from a video published by the Watchtower Bible Society (publishing arm of the Jehovah's Witnesses). Watchtower claimed that this was copyright infringement, and obtained a subpoena to force YouTube to reveal the identity of the maker of the video. The unnamed maker sought to cancel (quash) the subpoena, claiming that the video made fair use of the videos published by Watchtower, so no infringement action could possibly succeed, and that Watchtower had no legitimate reason to obtain his identity, and wished only to harass and discredit him for having questioned its teachings. (The allegedly infringing video expresses disagreement with, and attempts to ridicule, the teachings expressed in the Watchtower video.)
The district court found the allegedly infringing video to be fair use, and duly quashed the subpoena. Note that the unnamed maker could have used any of several other videos by Watchtower for a similar purpose, there was apparently noting unique to the particular video that was appropriated in part which was essential to the maker's use, nor did the court so much as mention any such unique aspect essential to the maker's purpose as being important to a finding of fair use.
As this answer bv Accumulation correctly points out, when a defendant uses more of the sourc work than is required to fulfill the purpose of the use, that weighs against a finding of fair use. But this is not an absolute bar to fair use (or anything close to one), as the rule proposed by user supercat would be. In several cases I have read court opinions that say, in effect "The defendant used more of the source work than was needed, adn that weighs against fair use, but the degree of transformativeness present outweighs that, so we find this to be a fair use." Thwe rule suggested by suoercat would not allow such findings. Excessive use leans against fair use, but is in no way dispositive.
I searched for any court case or law review paper which mentioned any such doctrine, and read through the fair use analysis in several recent court decisions in which fair use was found. I did not find any mention of the idea that fair use requires that the source work must be essential to the alleged infringer's legitimate purposes, and that those purposes could not be fulfilled by some other work, including perhaps a work available under a permissive license or in the public domain.
I conclude that there is not, and never has been, any such requirement in US copyright law to successfully assert fair use.