On the other hand, if we force all systems to be resilient to an internet shutdown then we'd end up regressing society by a lot. Think about how much more work a single doctor is able to handle more efficiently by having internet access (eg. charts, patient history, access to all the world's libraries) that would be lost without the internet.

If we don't force critical systems to be resilient to an internet shutdown, we'll be doing the meme. Specifically:

Weinberg’s 2nd Law:

If builders built buildings the way programmers wrote programs, then the first woodpecker that came along would destroy civilization.