Like many others have pointed out, I agree that I believe Rowling wrote the beginning of The Half Blood Prince to show just how much of a threat and problem this is not just for the wizarding community but for the muggle community as well. All the books up until this point have really just focused on the magical world and though there have been some muggles here and there who were caught in the middle, it was nothing that was too dangerous. I really appreciate that Rowling did take the first chapter to focus on the muggle side so that we don't forget that everyone can be affected by the magical community and it can have disastrous effects. As a muggle reader, I believe that helps put into perspective just how dire the situation could be for all of us.
I also like the fact that the Prime Minister had met Fudge before so we did learn that those deemed important enough as muggles are made aware of the magical community and events that could potentially endanger muggles. It reminds me of our governments today and how they hold back information that they don't think people would be ready or able to handle. I love the Prime Minister's reactions and I think quite a bit of us could relate to what we would actually do if some strange man just popped out of a fireplace and started talking to you about wizards and witches. It is a common occurrence in Harry Potter's world but not so much for the average person.