Why do we not reinvent the journal system?

I am very surprised that I could not find any similar question here.

It seems to me that researchers from all universities are willing to write papers about their research for free and hand them into a journal to gain reputation. On the other hand, some other researcher do voluntary check the paper in order to examine if the paper is acceptable for the journal. Therefore, the main work is done by researches.

The remaining work for the journal is to offer a platform where researchers can communicate and making sure that the reviewer is selected anonymous and to bundle many articles to a journal.

Now everyone has to pay a huge amounts for the papers, they are not accessible for free to the general public, even though that most researchers are financed by taxes and only the journal is making profit.

Now I wonder, should it not be possible to create a network page for researchers which contains methods to imitate the review process of a paper? So that all papers can be downloaded at the website for free. I guess most researchers would be very happy if everyone could read there work. Also the money that is spend on journals by universities could be spend to this huge network page instead in order to keep it running.