On the other hand, peer reviewers are generally paid by the same people who pay scientific journals--academic and research institutions--with contributing to peer review usually being an understood part of their duty.

In the case of ACM, we don't even have those costs. The conferences and reviewing is entirely community managed. The answer is: it's taxpayer and company funded, in an indirect way, by researchers contributing their time to do it. There are no paid editorial staff. These days, there's increasingly less paper involved, which eliminates the paper printing part of it as well. (those folks were paid, full time printers - but acm typically outsourced it to a printing firm anyway).

Very little remaining justification for copyright assignment to publishers.

In natural language processing, currently, research is published on arXiv and reviewed on Twitter. This is not how the institutions and funders involved would describe it, but it's what actually happens. If you're waiting for it to show up in a peer-reviewed journal, you're months or years behind.

Conferences are a good way to get caught up by letting the discussion of a number of papers happen in one physical place. The publishing industry is not necessary to organize conferences.

Journals seem to be a formalized mechanism for keeping score of the number of positive, novel results you've produced, in case you're ever up for tenure. Keeping score that way is not great for science anyway, because it biases science against negative results and replications.

When papers are discussed in the open on the Internet, you can see the discussion and choose who to believe. In formal peer review, you get the opinions of a few anonymous, uncompensated people, who would rather be doing something else, aggregated into a single bit.

The actual cost of the coordination is miniscule compared to the profits extracted in perpetuity from copyright. There would be more than enough money in the system to support those logistics if we stopped paying publishers in order to view our own work and that of our colleagues. When I publish, I lose the right to even view my own papers unless an institution pays for it on my behalf!