I don't believe a government-run AOL is likely to produce more benefit than the web Cambrian explosion. This proposal would lead to government blessings making things like AOL too big to fail.
I'm more saying we'd let the private market do it's thing, but then once we realize there's some core needs - search, basic social media, forums, etc - then we can make a public alternative that's free to access and run by the people instead of a private company that has to prioritize profits
I anticipated that was what you meant, and believe it would have a horrific outcome. AOL, but run like the DMV.