Somehow these journals need to be paid for their work. Peer review is not free, publishing is not free. Just putting it all out on the Internet for free is not a viable business model, as is proven by the many pay-to-publish crap journals discussed here many times recently.
While I agree with most other things you said, I think you got this completely wrong. Peer review is done by volunteers and publishing is relatively cheap (and the traditional scientific publishers make a lot of profit). You can easily operate a journal with very minor resources. And this is exactly the reason there are many pay-to-publish journals which are crap. It is just very cheap to set them up. But not all of these journals are crap (PLOS ONE is the most prominent example of a highly-ranked journals of this kind) and those which are crap are not because they are pay-to-publish. And many traditional publishers have crap journals too (remember the fake journals from Elsevier?). There is simply no direct relationship between the publishing model and quality.
The real reason the good journals are still mostly the traditional ones is simply momentum. As a scientist you need to publish in good journals to get attention to your work. The good journals get to select the most interesting research because everybody submits there first. And the readers (other scientists) read these journals exactly because it has the most interesting content. It is a self-sustaining cycle. Because - as you said - scientists have usually free institutional access to most journals, there is also not too much pressure for change. Only the public gets screwed because it does not get direct access to the research output and also because university libraries have to pay for the over-priced journals. But things are slowly changing because funding agencies start to demand open-access.