I am not a lawyer but I think it would be legally difficult to make it illegal to record what people say and do in public spaces. That was a right that the entire Western media depended on long before the Internet was invented.
The crux may be whether websites that require you to login to use them, like Facebook, are considered public or not. But anything you say or do in Facebook that you don’t restrict to being viewable only by 1st degree friends is probably considered public.
you are stating the current status quo as unavoidable - why is that?
Archiving everything has a massive cost and if it were illegal to archive unless people consent it would be much harder to get away with it.
When I post to a public forum I gave that forum rights to publish what I said, I did not give everyone else the right to store what I said