I am not one of the most radical signatories to the “Cost of Knowledge” statement: there are certainly some among us who look forward to a world without commercial journals, or even a world without journals at all. I don’t yet see a clear path to that world.
Nonetheless, I want to add one possible item to the case against journals.
There is lots of inequity in the way mathematicians are assigned status — we all have researchers we think are underappreciated (and some people are quite willing to talk about who they think is overappreciated.)
One very simple source of inequity — but I’ll bet a pretty large one — is that authors decide what journal to submit to. Some people “aim high” — their method is to ask “what’s the best journal where this paper would fit?” Others “aim low,” asking something more like “what’s the median journal where papers like this appear?” You can’t get in the Annals unless you submit to the Annals, and you won’t submit to the Annals very often if you aim low.
Women in the workplace are socialized not to ask for things. I wouldn’t be surprised to learn that there are disproportionately many men in the “aim high, why shouldn’t my paper be in the Annals?” group. (And of course, for those who get het up whenever I talk about women in math, this applies just as well to any group of mathematicians disinclined to push for their own work.)
Would things be different if papers in the Annals were selected from all papers, not just those whose authors decided to nominate themselves? Then publication in a top journal would be a little more like being invited to speak at a prestigious conference. Would that be an improvement?