I disagree, and strongly. Future historians will probably disagree with you too. Even the most inane TV shows can prove to be extremely valuable when trying to decipher the culture of various countries 300 or 3000 years in the past. Imagine reading a trashy romance novel from 1000 BC. You'd learn a lot about the people who lived in that time.
You might counter this by saying that with all the information out there now, we only need to keep the "good stuff". But who decides what's good, right now? How do you know that what you decide is good will always be seen as good? Your personal opinions on the content disappearing are totally irrelevant when perhaps millions of people have seen it or have been affected by it.
All information that is created should be saved, especially since we're able to. Imagine the ancient Romans deciding to burn a bunch of books because it cost too much to hire guards for the library. Ouch.