That’s already exactly what they do.
Unfortunately the attackers often still don’t stop right away. Keep in mind that a DDoS attack is a really crude but really effective way to take down a server. The attackers want the server to stay down as long as possible, and won’t let up just because they’ve knocked it down. The only real advantage to taking the entire server or receiving IP addresses offline manually is the fact that it protects the server from being physically damaged from an overload. But the sites are still down which is what the attackers wanted all along.
Unfortunately DDoS attacks are just really difficult to stop. Protection services like Cloudflare can help you against them, but they’re useless if an attack is already reaching the server directly.