Norway would, and does! https://en.wikipedia.org/wiki/National_Library_of_Norway

All media published in Norway (includes streaming) is required to have a copy sent to the national library.

Edit: Though any licensed media is only available on their network, sadly no taking home. Though things like news papers are publicly available anything from 2 to 7 days later. (when it’s irrelevant)

Norway actually does this: https://en.wikipedia.org/wiki/National_Library_of_Norway

Any and all media published (includes streaming) in Norway is required to be supplied to the national library.

It’s quite neat, they’ve discovered some lost media in their archives a couple times too, this is one example: https://www.thehistoryblog.com/archives/33888

Edit: Though licensed content is not accessible outside their networks, can’t stream the latest episode of your goto TV show for free online at home.