Should all public online content be catalogued for future generations?

Currently, nearly every piece of printed matter whether it is a newspaper or a book is catalogued and stored. Everything that can be read, usually winds up in a depository so that down the line someone is able to go back and read it again.

My question is should this be extended to all public online content that can be read.

Should we be storing blogs, online photos, tweets and so on in public repositories, so that they can be available to future generations.

Given how much content is now online trying to store it all now, let alone in the future would be a massive job.

Does the sheer scale of it make it an impossibility, is the majority of the content so terrible that trying to find the diamonds just isn't worth it?

Or regardless, it is worth storing all that accumlated, knowledge, thoughts and wisdom?

I think overall it would be good if it gets stored. I don't expect it to be 100% though.

Here is my thought on why it would be good, eventually there will be projects involving vastly more powerful computers that will use Algorithms not yet written to make huge sweeping generalizations about this early phase of the communication age and especially the Internet. This will probably prove valuable to future historians where they will have huge amounts of information about how people felt about the events of the time as opposed to a few newspapers and letters on given events.

Is this a great boon to humanity? No I don't think so, I think it is more of a "This will be useful thing."

I think, whether we want it to be stored or not, it eventually will. Maybe not everything we have right at this moment, but as memory becomes cheaper and more convenient, it will happen. It will simply because easier to save things on the off-chance someone will want them someday than to delete them and risk losing some tidbit that will later be wanted.

It's going to be less about "should we" and more "we can, so we will."