The production of news content -- like aid to the destitute or the military -- might be an obsolete business model but is still an essential social good worth protecting.
When you write what appears to be "I think all currently viable options for funding serious news production are inappropriate", then it doesn't sound like you value news content. That is honestly an attempt to not strawman you, just a (perhaps confused) understanding of your seemingly untenable position. If an alternative to state funding is viable while still allowing free aggregation and distribution by arbitrary third parties, I am definitely interested in it.
Having an educated populace has enough value that we have public schools; I don't see how informing adults is any different.
Note that I think there are also a ton of unrelated recent societal changes that make it not economically feasible for the news to be behind a paywall; notably that recent shifts that have dramatically reduced cost of publishing and aggregating have made it extremely easy to republish other journalists work trivially. All you need to do is have a subscription to the NYT paywall and one guy getting paid shit to reword their articles; to any other user they will choose the free content that has the same core information that the other site could never have afforded paying for investigative journalism. Patents on reporting facts are obviously untenable, so I see no real option other than the state supporting the media.
Who says it is outdated? Do you have stats on that? I get more news content now than ever before. There clearly must be money in it, or enough that people haven't stopped producing content.
Also, who says it is a societal good that we must protect? If society no longer values news and refuses to pay for it, who are you to decide we still should?
There will always be demand for news, it just depends on where the demand is.