As someone who is on the editorial board for 3 journals, reviews about 3-4 papers a week, and is not a faculty member (I'm a contract researcher) with over 50 peer reviewed publications to his name, let me tell you about some costs you're missing in your assumptions.
1) You're correct that the peer review process is provided free by scientists like myself, and it is our duty to provide this review. However, I'll spend 1-3 hours on a paper reviewing for content. What I'm not doing is copyediting. You're assuming that the papers submitted are in good shape when they arrive, and I would say out of the hundreds of papers I've reviewed over the years, only rarely have I found one polished and ready to go. Almost all of them have formatting errors, typos, and grammatical errors. The worst ones sometimes are those where the author is not a native English speaker. They could have absolutely fantastic results, but the spelling and grammar is so bad you can't exactly figure out if they've discovered something novel or if their results are totally bogus. You need to pay for someone (or multiple someones) to clean up, copyedit, and format each paper.
2) Electronic review system. I'm not seeing how your model pays for this. Someone has to pay to host, maintain, and power those servers - they don't set up themselves. That is a cost that can be divided per paper submitted to the journal - but then onto #3.
3) Many of the open-access journals make the author pay to submit the article upon acceptance to the journal, thus paying for items #1 and #2, but with budgets being cut you're asking the author to sacrifice even more of his small budget (which in my case pays some of my salary). So who pays in the end is always going to be a sticking point.
4) Not all peer review is fast. You're assuming all scientists are ideal and get right on the paper as soon as they get it. I've had papers that came back in a week, and others that took 9 months (reviewer #3 sat on it and the editor couldn't get them to follow up after they had accepted the invitation to review). So you need to pay for some infrastructure to either pull the paper back from the offending reviewer, or pay for automatic reminders and follow-up.
I personally like the existing system as is - it works well for me and I can usually rest assured that the content which does finally get published is polished and ready to use. But I'll agree that the journal costs are not sustainable. What I'd rather see is that after 5-10 years, any federally funded research automatically becomes public domain. That way the journal publishers make their funds to sustain the quality of the journals (and I'm talking print quality here only) and the system continues to run smoothly, plus the public domain gets to build off of the results that we as taxpayers paid for.