Why is it acceptable that publishers sell papers they didn’t pay for?
History.
In the dark ages (i.e., before the internet), publishers provided a valuable service. If an author has a great idea, they want the whole world to read about it and the best way to do that is to get someone to publish their work. The publisher arranges for reviews, copyedits your work, and, most importantly, prints thousands of copies and sends them to libraries and archives around the world. (Note that, legally, they need to have the rights to distribute the work, and they claim ownership of the copyediting work.) Doing all this printing, mailing, and copyediting costs a lot money and thus publishers have to charge for their services. They also make a small profit from all of this.
Fast forward to the 21st century and the picture has changed considerably. Since the arrival of personal computers and software like LaTeX and Microsoft Word, copyediting is now mostly done by authors. (Reviewers and editors are rarely paid.) And, due to the internet, it is very easy to distribute papers using websites like arXiv. Going to the library to find a print journal is now a thing of the past, as journals these days just have websites. Of course, publishers are still doing something, but it's a fraction of what it used to be.
Publishers made a lot of sense 50 years ago, but these days their model doesn't make a lot of sense; they still collect a lot of money, even though the services could be provided much more cheaply. So why does this model persist? Firstly, publishers still own the copyrights to lots of old work that is still relevant. More importantly, publishers own the "prestige" of their journals, which means academics keep sending them their work.
It is not acceptable, and people are taking steps to change things, but the system has enormous inertia and many perverse incentives that must be overcome to make progress.
I would like to draw an analogy to fiction publishing. Authors in that field have a maxim called “Yog’s Law” which states: money is supposed to flow toward the author. This is held as a guiding principle, even in contexts where nobody expects to make a living by publishing their fiction: short stories, for instance, pay a pittance (SFWA minimum rate is US$0.06 per word, times one to ten thousand words, so $60 to $600 for a story that probably took at least 40 hours of effort to write—this is beer money, not rent money). This principled stand is because there is a long history of “vanity presses” scamming authors with grandiose promises of riches and fame if they’ll just underwrite the up-front costs, and then not doing any marketing whatsoever, so nobody buys the book and the riches and fame never materialize. Contrast this with a legitimate traditional publisher, who pays you an advance, assumes the risk that the book never sells enough copies to “earn out” that advance, and does do marketing. Also contrast a printer for hire catering to self-publishers, who will tell you up front what services they do and don’t provide and how much each costs, and will not make any grandiose promises. This is who you should hire to print up your family history, not a vanity press—unfortunately there isn’t an accepted alternative term for honest printers-for-hire as a group..
Academic publication is different because not only do we not expect to receive riches from publication, we don’t expect to earn anything at all in the first place (for journal articles, anyway; I understand monograph and textbook publishers do pay royalties). Yog’s Law does not directly apply. However, we are looking for a particular kind of fame, the kind where other researchers read our papers and learn things and build on them, perhaps even centuries from now. (Much as a writer of fiction hopes that people will read their stories and find entertainment or catharsis or inspiration in them.) For this reason, we warn against publishing in “predatory journals” that charge hefty fees, don’t do adequate peer review, and exaggerate the likelihood of anyone reading the paper or taking it all that seriously. Predatory journals are the direct analogue of vanity presses in academic publishing. They don’t provide value for the money.
Traditional academic publishers are supposed to provide value for the money they charge: peer review, copyediting and typesetting, archiving, dissemination, and perhaps most important, reputation. Any paper published in one of the top journals or conferences in my subfield has a good chance of being worth my time, and I rely on that. However, over the past 40 years or so (I’m not old enough to know exactly when this trend started) the publishers have become less and less interested in actually providing value, and more and more interested in extracting rents. This is really obvious in my particular subfield, computer security: as I write this, I’ve got a paper accepted for publication in an ACM conference with a top-notch reputation. They facilitated the peer review, but they didn’t pay the reviewers a dime; they did none of the work of copyediting and typesetting, expecting me to hand them a PDF already fully formatted; they maintain both print and online archives, but they want to either charge every reader US$25 for the privilege, or charge me $700 up front. I know that this is price-gouging, because if I had published the same paper at a USENIX conference with a similar reputation and providing an identical set of editorial services, they would charge either readers or me nothing for the privilege.
The usual market-based solution to rent-seeking is refusal to cooperate. So why are we all still cooperating with them? It’s a classic collective action problem. As long as most of the researchers in a field continue to publish in traditional venues, any one person can’t refuse to do so without nasty consequences for their career. If everyone threatens to stop all at once, on the other hand, they have a chance of at least extracting concessions—in my time in graduate school, many of the top computer security conferences have moved from paywalled to open access, because our community put its collective foot down. (Not without incident, though, as anyone else who attended the business meeting at Oakland 2011 can attest.)
It is acceptable because there is no convincing argument why it should be unacceptable.
More generally, there is a principle of the law that people are free to enter into contractual agreements with each other, and with other legal entities such as corporations. As long as those agreements are entered into voluntarily between people of legal age, and as long as they are not deemed to be unconscionable agreements, the agreements are legally binding, and in that sense “acceptable”. Other people who are not parties to the agreement may occasionally find them objectionable and be unhappy, but that’s their problem.
In the case of academic publishing, authors voluntarily agree to let publishers publish their papers and not pay them any royalties. I have done so myself many times. So, if I find it acceptable to not get paid royalties for my papers, and there isn’t some convincing legal argument for why my agreements with publishers should be declared unconscionable (as far as I know no one has tried to make such a case), then that’s the end of the story - it’s acceptable.
As for why I and other academics don’t have a problem with not getting royalties, I think the answer is a bit too complicated to discuss in detail here. The short answer is that writing papers is part of my job, for which I am paid a salary by my employer. Scientific papers are simply not the same as fiction or other forms of writing that people write to make money through a direct sale of their work to a body of readers. Your question assumes a premise that publishers should pay scientists for their papers because of the superficial similarity between academic publishing and other types of publishing, but that premise is simply false.
Edit - some additional thoughts related to the (very interesting and thought provoking - thanks!) comments:
I want to clarify that the main point of my answer is to emphasize that the answer to questions of the type “why is activity X acceptable?” is generally “it is acceptable by default” - that is, it’s up to opponents of X to convince everyone else that X is not acceptable if they believe that’s the case, and until they successfully do that, X is acceptable. I consider such questions to be loaded questions, since they subtly insinuate that there’s something wrong with X (without actually giving any explanation or evidence) and put people who engage in X on the defensive to “justify” their “bad” behavior. I think this loaded question effect is what makes the question “annoying” (as @Allure referred to it in a comment).
In my answer I was trying to make the point I elaborated on above. I focused on the legal aspect just because that’s what occurred to me at that moment, but the same principle applies if we were to debate the ethics of the issue (as some of the answers have done). I do acknowledge that there are some valid ethical criticisms of some of the practices of the academic publishing industry. But in my opinion those criticisms (while very interesting) are tangential to OP’s actual question. OP asked:
Why is it acceptable that publishers sell papers they didn’t pay for?
Note that this isn’t asking why it is acceptable for some publishers to make as much money as they do (I think there are some reasonable arguments to be made that that may very well be unacceptable). It’s asking why it’s acceptable for authors to not get paid by publishers for their work, which is a different question. Well, as an author who voluntarily publishes his work without asking for or expecting to be paid royalties by the publisher, I find this a bit offensive, as it’s effectively accusing me of being complicit in an activity insinuated to be shady or immoral, or alternatively suggesting that I’m some sort of victim of predatory practices. I’m neither of those things.
The most correct answer in my opinion is the one in David Richerby’s answer, which is to point out that this is a loaded question based on a false premise. I expanded on David’s idea a bit more. The bottom line is that it’s acceptable for authors to let others publish their work without asking to get paid, and it’s acceptable for publishers to publish works that authors allow them to. The larger debate about academic publishing is an important one and will go on, but this question is (in my very humble opinion) not framed in a way that makes it a helpful part of that debate.