Rephrasing the gist of your argument: The professors are overloaded, so they cannot do a thorough job when they are on a hiring committee. Therefore, we should use the existing structures that make it trivial to rank applicants, with the unfortunate consequence of us supporting the closed-access journals of today.
My biggest disagreement is with the "Therefore" implication, and allow me to illustrate why.
As a PhD student, I am also obligated to teach (T.A., mostly). The hiring process we mentioned completely ignores teaching skills, and at my uni there is very little negative feedback if you do a "modest but not very good" job.
Therefore, some PhD students actually do not think too hard about their teaching, and just reuse exercises that were given last year, so they can do other things (research). Not all PhD students do this, mind you, but it is clearly a good strategy if you want to get hired.
You can use the same argument you just made to say: "The students are overloaded (they are), therefore we should be okay with them doing a sloppy job when teaching." But is it something that you can actually agree with? In my opinion, we should come back from the other way: The teaching has to be good, so we have to give the students enough time to prepare and not overload them, so they do a good job at whatever we assign to them.
And this argument translates to the professors' case as well, at least for me. The hiring process has to be fair, and the research has to be free, so we should give enough incentive to the professors on the scientific board to spend enough time so they do a thorough job. Or maybe invent new ways of ranking, so that we do not depend on the closed-access journals of old. Either way, we should not give up open-access research just for this triviality.