As someone else pointed out, losing information is bad because we can't know what value it might have in the future, only what value it has to us today. A lot of things from the past that we are certain had no value to people at the time (such as literal garbage heaps) are of immense value to historians today in understanding the past and the context within which those "worthless" things existed.

You're right though that a decision will probably have to be made at some point about what to keep and what to toss (how big is YouTube, exactly? Are we really going to keep every video, in its original resolution, forever?), but this is just plaintext, it takes up almost no space. The decision doesn't even have to be made, since it's easy to find the means to store this, so why bother making it? Kicking the can down the road is actually the best decision in this case, since the people of the future will (hopefully) have a clearer understanding about what was important in our own past than we do currently.