Payment for articles in journals The mainstream academic publishing model assumes that authors are somehow paid by third parties (typically universities or industry) for the time spent on research. With increasing casualisation of the academic workforce (particularly in the humanities) this is arguably less appropriate than it once was, and many authors are no longer paid for the time spent on research. Amongst other things, this has strong negative consequences for diversity, as it biases the system towards those who can afford to work 'for free'.
An alternative model could involve authors being paid directly by journals for their submissions (as is common for, say, freelance journalists). Has this ever been tried in academia? Is it a realistic possibility?
I am not aware of any journals in my field (physical sciences) that would pay cash to authors for research papers. There are some obvious edge-cases:

Some major journals such as Science/Nature contain a certain amount of non-research content, e.g. 'science news' and commentary on policy matters. I presume that the authors of this material get paid fairly directly for their efforts to produce it. However, one might argue these individuals are acting as 'journalists' rather than 'academics' when they do so.
Some journals carry book reviews. I think it is fairly common that the author of the review gets to keep their review copy of the book. For a major textbook, this may have non-negligible financial value.
Some grants/awards, especially those from professional societies, may come with some obligation to contribute a report to one of the society's journals. However, the award is not (in any case that I know) expressly claimed to be payment for the journal contribution.

Researchers in certain areas have opportunities to profit from private consultancy arrangements with industry/commercial enterprises. In some cases, this may entail conducting and publishing studies with a particular focus (typically, to prove that the company's products are safe/effective/better than the competition). Anecdotally, this is particularly prevalent in medical fields. Of course, there are many potential ethical issues here.
Otherwise, the general assumption in the physical sciences is that authors do so in the course of their employment at a university/research institute/company, or as students working towards a degree (for which they may receive some scholarship/grant). Of course, there is a big difference with the humanities here, due to the relative abundance of research funding for the sciences.
That said, it is interesting to note that publications are (largely) required only to get or improve a job, rather than to keep it. An academic who habitually failed to show up to teach their assigned classes would likely find themselves facing disciplinary action. However, an academic who fails to publish rarely sees any personal consequences until the next time their employment falls to be reviewed  (either as a tenure/promotion/contract renewal case, or because they've applied for a new job).
I presume the premise of your question is that many academics have teaching-only contracts, and therefore any research they do is 'in their own time'. The issue here, as I see it, is that people who want one career path (academic research) are being encouraged to take a different one (academic teaching) and view it as a 'stepping stone' to research. This is a huge problem, but I'm not sure that either the blame or the solution lies with the publishing process.