How would you publish if you're not a part of a major research institution? Los Alamos National Lab could host its own papers just fine, but what about small-time labs? I know of at least one person who doesn't even officially work in science but publishes original research they do in their free time.

The journal system still provides a service, even if they over-charge for access. The peer review system has value. Imagine if there was zero barrier to publish. As a reader, you'd have to wade through piles of trash to find decent science.

Where would you find it all? Currently we use journal aggregators, whose service also has value and costs money. Are you really going to go to every university's website looking for research relevant to your area? We could do that again, but with everyone responsibile for publishing their own work, well, who gets indexed with the aggregators?