Here's why: Let's assume we have the perfect algorithm that knows exactly which sentences to pick for a good summary. You'll still end up with a summary that's horribly out of context and difficult to read.
Try it yourself. Assume your brain is the perfect algorithm and pick the most important sentences for a summary. Then try to read just the sentences that you picked without rewriting it into a coherent paragraph. More than likely, it'll be an out of context confusing block of text.
Algorithms will never solve the summarizing process unless they are teamed up with a rewriting engine that could build coherent paragraphs.