Well, think of it like a security checkpoint at the airport - it's all about keeping everyone safe and sound. The US Tennis Center wants to make sure that all spectators have a great time, without any, ahem, unsportsmanlike conduct. By regulating what you can bring in, they're able to minimize any potential risks.
It's kind of like when you're going to a music festival - you know, where they have those strict rules about what you can and can't bring in? Yeah, it's similar to that. The US Tennis Center just wants to ensure that everyone has a blast, without any, you know, bag-related drama.