I’m surprised nobody has done it yet, there must be some stumbling block I’m not aware of.
The current publishing model is a frequent topic of conversation among my colleagues. We share and discuss papers (formerly on Google Reader, now using substitutes like G+) from many sources. I would like to see http://arXiv.org acquire a public review process.
Two things need to happen to change academic publishing:
1. Being a peer reviewer for a corrupt journal needs to be viewed not as a feather in an academics cap, but as a contribution to a corrupt system. Basically reviewing Elsevier journals should hurt your carrier not help it.
2. A new system of publishing needs to arise based on well-compensated (and hopefully more effective) peer review and cheap access.
Start-ups can address #2, but you will be dependent on high profile academics like Gower constantly speaking out against the old system.
Why hasn't it happened yet? I assume that Elsevier has a stick to hit the top people with (either a contract, or it's funding them).
The whole academic culture needs to be changed. People like Gowers who already earned their stripes can begin to change attitudes. 99% of mathematicians can do nothing except hope they can get a permanent job one day. And even then their institutions are going to force them to undergo yearly evaluations where they have to give an account of what papers they wrote that year (too bad if you are working on a multi-year breakthrough) and whether the papers were published in journals they deemed respectable (universities are also competing with each other for prestige).
Another problem is that too many mathematicians are devoutly religious when it comes to speaking out. Any kind of rocking the boat is likely to affect your karma (chance of getting tenure/promotion/funding).