If no money is changing hands; who's gonna edit, typeset and print them? Who is gonna manage mail, comments from readers and so on? Pimple-faced volunteering undergrads?
I think desire to have everything free is a fantasy of the open source community. Not everything can be run like open source software project. Sometimes people need to get paid.
If you look at the list of names, those are largely math and computer science academics - the very people who produce such papers and articles.
I think you have a fundamental misunderstanding of how academic journals are structured and managed. The editing, typesetting, handling of communications and such are all done by the academics themselves. And those academics are not paid by the journals.
In most academic publications, the editing, typesetting, managing mail, etc is done by the volunteers or the papers authors. Pretty much all journals are going online only so there's no need to print anything.
In short the publishing houses do sod all, and get paid a lot of money for doing sod all.
The editors, most of whom are minimally paid and do it for prestige. I.e., the same people who currently do it.
...who's gonna edit,
Unpaid referees/editors, the same people who currently do it.
...typeset...
Authors, the same people who currently do it:
\usepackage{freejournal}
...and print them?
Readers, the same people who currently do it. Or are you imagining that there is some pressing need for physical journals to be printed and delivered to libraries?
It's true that sometimes people need to get paid. The point of the boycot is that in fields like Mathematics these people already work for free.
The only thing Elsevier does is archival and distribution. Editing and typesetting is done by the authors themselves, who provide camera-ready copies. I do not believe the publishers ever get involved in managing mail. The reviewing of paper is done for free by academics. It is coordinated by an academic on the editoral board of the paper. Even these editors mostly work for free or for some small compensation.
While Elsevier do provide some service (archival and distribution), their service is in absolutely no relation to the cost. The difficult parts of the business are already done by unpaid volunteers.
One would hope a philanthropic organization (e.g., the Bill & Melinda Gates Foundation) would step in and help support an open system. If the vast majority of labor is already pro bono, the money could be spent setting up an infrastructure.
I think desire to have everything free is a fantasy of the open source community. Not everything can be run like open source software project. Sometimes people need to get paid.