How do researchers get paid under the current system? My understanding is that the journals do not pay the scientists that produce the articles. Am I mistaken in this?
You're not mistaken - journals don't pay researchers or reviewers. If they did, I'd be significantly less upset by their practices. As is, they get their product (papers) and their skilled labor (reviews) for free.
Elsevier had a 36% profit margin last year, which is a pretty clear signal that they don't face sincere costs or competition.
They are paid ether by their respective universities/institutions/companies and/or they pay themselves from the grant money they were awarded for a specific project.
But the key point is that they're not paid by the publisher for the publication, they're paid to produce the publication by others. The publisher is just gets it for (basically) free and then profits off the fees.
Are we counting only monetary payments? I'm assuming there is some benefit that is given to the scientist for publishing, especially in cases where the scientist pay to publish. It isn't likely at all a simple relationship between two parties, but I doubt that the scientists are being irrational by using a publisher.
Sure, but how does paying the publisher enter into this? The scientist may well be happy to have their paper shared freely after publication, since they receive no reward from the publisher. Scientists are only being irrational if they have choice in the matter. If they are forced to publish by the community / university, they may well resent being forced to use such publishers.
Elsevier had a 36% profit margin last year, which is a pretty clear signal that they don't face sincere costs or competition.