I would imagine that reviewing papers for free is usually considered part of 'service' to the field and the imagined tradeoff here has far more to do with whether the journal is influential or not, and almost nothing to do with pay or access policies.
And you have to submit your work edited and almost ready to print, it's not like they are doing heavy work there either. I remember one time I submitted an image as SVG but they wanted EPS and asked me to do the conversion. Yes, that oneliner with "convert" was enough.
Are you asking if they will be reviewing papers exclusively for open access journals and avoiding non-open access ones? Or something else?
* The American Journal of Epidemiology * Epidemiology * Infection Control and Hospital Epidemiology
Those are the journals of the Society for Epidemiological Research, the International Society for Environmental Epidemiology, and the Society for Healthcare Epidemiology of America's journals. I am a member of all of those societies. I would, to be frank, rather like to be on the editorial board of those societies - and certainly wish to be on good terms with their editorial staff. And revenue from those journals does help support the mission of the society.
That's the benefit. "Going on Strike" would harm all that, and in my field, the vast majority of papers will be open access within a year anyway (due to NIH/CDC funding).
While cross-domain sharing of insights and knowledge is commendable and important, I'm not sure why it would make sense for review to be outsourced to non-experts in the field, as you describe (even if the paper was "readable" the domain experts would presumably be the most able to evaluate a paper). Maybe one or two reviewers on a panel of many, but otherwise it makes very little sense. All of these suggestions essentially serve to slow down the research process and have benefits for a very small portion of the potential audience.
I think what is more valuable to opening academic research up is greater open education material, besides the traditional models of bachelor->masters->phd->postgrad, and more aggressively written textbooks that work on the cutting edge of the field (with appropriate disclaimers).
Oh, and big disclaimer: tons of papers are badly written. That doesn't affect any of these points.
Some groups have a (never large enough) budget to fund flyers, posters, videos, websites, etc. for public outreach and visits to public events. It's also usually possible to ask for this kind of fund when applying for research grants - like adding an extra 3% on top of what you ask for in order to publicise the work.
[1] https://www.ligo.org/science/Publication-GW150914/index.php
(Usually, if peanuts are involved, they're literally peanuts)