FBI logs one million bot IPs

Just how many zombie bots are out there? While exacty numbers are of course impossible to acquire, the FBI knows of at least one million. That is, one million they know about doing something naughty. Of course, just about every last one of those is an infected machine, with the owner blissfully unaware of their machines wrongdoings. The FBI, along with many other agencies and companies (such as just about every ISP in existence) has a huge incentive to take down botnets, as they are often used to inflict DDoS attacks on undeserving targets.

Patching machines is one thing, but there's a lot to be said about ancient machines never upgraded that perhaps are still running Windows 98 or Windows 2000, open to the Internet, On top of often being used as bots, infected machines are also often used to host phishing sites or other scams. Is there a long term solution, besides trying to track a botnet owner down?