Existing libraries already have trouble with low-quality books and film that doesn’t survive very well. Only the most important artifacts tend to be copied to archival-quality material.
Why would digital artifacts be any different? And where is the incentive to preserve this stuff? Look at how much bitrot there is on most web pages after just 10 or 20 years. Even setting aside physical bitrot, there’s plenty of semantic data loss that nobody really cares enough about to fix.
Finally, despite all the above, let’s say we do come up with a cheap and practical way to store digital data for very long periods of time. Unless it’s very compact, it will use an appreciable amount of energy and material resources to store stuff. Which tiny fraction of the massive tidal wave of digital content should be archived, and who gets to decide?
To my understanding there are institutions including the library of congress whose main purpose is preserving information. Not all information, of course.