It is not. It is only for us normal people. But the companies which log our lives in order to then capitalize on it, for them the internet is not ephemeral. They have copies of videos, pages, podcasts, whatever it is what can be found there.
Why would you want those companies to know more about yourself than you do?
I'd also hazard to guess most people in this camp would want these companies to also not store these things the same as they don't want people to.
In a the Internet is both too ephemeral (self-hosted blogs disappear, Youtube videos get taken down) and too persistent at the same time; I don't think that most Twitter posts of non-public figures would need to remain public forever by default, for example, and I don't think I need to mention various data breaches.
The Internet Archive somewhat mitigates the first issue, but it makes me pretty nervous that there's essentially just one organization doing what used to be much more distributed to various physical libraries.
For the second one, I hope we'll see better solutions (both technical and social) as the technology and our interactions with it mature.
That's not a question of wants, companies will always know more about you than you, for the simple reason that even if you had all their data you have no means to extract any meaning from it. It requires immense organization and resources, increasingly so as the rate of data production increases.
For that reason the correct response isn't to engage in the same hoarding and privacy abuse of the companies, it's like bringing a knife to a tank fight, but to 1. make sure you don't produce that data to begin with through privacy protections and technical means and 2. create environments in which you have ownership of your data, instead of businesses.