How is this new? Have you heard of botnets? Read the "spam capacity" figures for the largest botnets, and you will see that not only is this possible, but if you have the money and connections to find the owners of the botnets, it could be done tomorrow.
But the internet itself won't be destroyed. You couldn't possibly target the millions of servers out there simultaneously, and taking out individual pieces of infrastructure would only mean a temporary loss of capacity.
The internet is built on trust that individual users won't abuse their bandwidth by using 100% of it all of the time, and that ISPs will identify and restrict users who do so. As it is, most of the spam and DDoS attacks come from three or four rogue ISPs out of the hundreds. Putting internet-wide restrictions and "countermeasures" destroys the fundamental freedom of the internet and would reduce its creative and economic power.
The main way to reduce botnets in general is diversity of software. No software is invulnerable to security holes, so when one surfaces it is bad to have 90%+ of computers vulnerable simultaneously. So I think one of the most effective measures we could take is to end the single-company domination of the PC market and have a wide range of OSs, server software, and hardware architectures availible. I'm not specifically saying MS is worse; a >90% Mac OS X market would be just as vulnerable.
