The arXiv and wikipedia are not the only alternatives to paid, publisher controlled journals. There are a growing number of open access journals which have the same quality standards as any publisher controlled journals. Additionally many publishers have gotten into the habit of mass producing really poor quality journals to include in packages that libraries are forced to purchase to get other big name titles. All of the quality of a journal comes from the academics who almost always but the editing, peer review and writing in for free (or technically university time). The only real service publishers ever offered was the ability to create print journals, but that is not longer necessary (or even desirable).
What you and several other people are missing is Journals don't spam reviewers with random studies. They put some effort into finding an appropriate group of people to review the research which both reduces the reviewer workload and prevents inappropriate people from reviewing things. Also reviewers gain an early look at research appropriate to their field of study, which granted is still mostly junk but far better than random.
I don't think this is going to be hard to replicate, but it's still reasonably expensive to do well for a for a large number of articles, so I suspect open access would require at a minimum a few hundred dollars per submitted article worth of work which can’t exactly be add supported.
The thing is there are already millions of dollar per university library going into paying for serials. Publishers make a huge profit. So the real issue is finding a model where universities can more effectively redirect that money towards open access. However I'll be the first to admit that getting universities cooperate even if it's in their collective interest is no simple task.
