First of all, this wasn't about a service on the internet, but a P2P network. I want to download and upload data over BitTorrent, or to have conversations over TeamSpeak, but that doesn't mean I want to manage my PC like a public server.
Having a public server on the path, which is what hole-punching does, helps with this, especially in the area of DDoS, since attackers first have to fool the hole-punch server before attacking any specific peer directly.