In fact, academics don’t get paid by databases, journals, or anyone else that publishes or hosts our work. In the case of journals, we’re often the ones who pay publication fees. Those who write textbooks get royalties, but that’s about it on that front.I grew up with a father who was a professor and a mother who was a university administrator who helped professors get grants for research and comply with human subjects requirements, so I've know this for as long as I knew it was something to know about. But, lots of people don't realize this fact.
Now, this doesn't mean that professors don't receive economic benefit from publishing. The business model of academia works like this:
1. You need to do research, ideally publishable in some form, to earn a PhD, and a PhD or good progress towards earning one in the very near future, is the basic prerequisite for being hired as a professor.
2. Professors are initially hired for one to three year fixed terms as lecturers or as tenure track "Assistant Professors".
3. An Assistant Professor is evaluated for tenure (usually after three years, but practice varies and sometimes there are multiple stints as an Assistant Professor at the same institution or successive ones). If you get tenure, you are usually simultaneously promoted to "Associate Professor" and get a raise. If you don't get tenure, you may be given another shot, but usually, you are terminated.
4. An Associate Professor with tenure can then be evaluated for promotion to full "Professor" with greater prestige and higher pay.
In all of the main career steps in an academic's life: getting a PhD, getting hired as a tenure track professor, earning tenure, getting promoted to Associate Professor, and getting promoted to full Professor, the dominant consideration is what research you have published in peer reviewed scholarly journals and how significant that research is (e.g. measured by citations in other scholarly work). There are other factors, but that is the dominant one. Hence the phrase, "publish or perish".
Your publications are also the primary consideration in how prestigious and high paying a post you will be hired at (often after landing a first post elsewhere) and of your prestige in your field and the academic profession in general.
A professor at a research university has a teaching load expected to use about 25%-67% of his or her time, with the most esteemed professors having the lightest teaching loads. In the balance of your time you are expected, but not required (once you have tenure) to do research, most of which should be potentially publishable in peer reviewed journals.
Subsidies for universities and colleges from state governments that make this possible is the main way that state government finances basic research.
So professors have strong incentives to publish, but are not directly rewarded for the publications themselves (many of which have arguably weak claims to intellectual property protection due to exceptions for factual compilations and scientific principles).
This is a good thing, because, in the end, their incentive is to produce more papers, not necessarily for those papers to have lots of readers, and even very respectably cited papers are often read by a very small number of readers and purchased by few customers other than academic libraries.