The internet is effectively a monoculture. A well placed attack or ten could disrupt enough of the system to effectively make it useless. This seems like a really bad plan to me. Several years ago, really fairly early on in the progression of the Web, I worked in a small office. Even in that archaic computing/communicating environment when we lost internet access, even though we had office and cell phones, work pretty much stopped. It is worse now.
I would suggest that on some fairly basic level the internet needs to operate on more than one protocol. The first and most obvious addition would be the addition of mesh networking protocols to all major operating systems. That would allow a fairly seamless transition to peer-to-peer networking in the event of catastrophic system failure. Given the proliferation of large capacity external drives, much of the Web's information could be distributed and remain accessible. The mesh networking would probably work best on the wireless networked computers but it should be possible to structure it so that hardwired computers are also visible.
There are obviously other changes that could/should be made to increase the robustness and resiliency of the internet. It should be a high level priority in government and in business.