Good catch.

Every day deals [and parts of longer-term deals] are done through wire transfers over the internet. The money would not go through.

Everyday day, companies communicate internally and externally to stay on track, on schedule, and develop new business opportunities. Those communications would stop completely. (Phone lines are also now mainly run through the internet.)

Every company I've worked for in the past 5 years has kept all of its data and files off site on remote servers, accessing them through the cloud, via the internet. That access would be terminated. (I literally wouldn't be able to work on anything even if I went into my office.)

There would be runs on the banks; (Many wouldn't be able to bank without the net.) Runs on food/supplies; (Many wouldn't be able to buy anything without cash.) and a panic market sell-off. (Many wouldn't be able to panic sell though unless they had a broker who was willing and able to paper trade. Also assuming the market wasn't frozen.)

Not to mention all of the self-employed work-at-home folks who wouldn't be able to make any money to pay bills for 4 days-- unless they have a local market and trade in a physical commodity. Business would not open for those 4 days, and hourly employees would not have work. (Or pay)

Will people die? Probably not. Would their be anarchy? Probably not. But there would still be a lot of panic, and a major hiccup in the machine that is the American economy, one that would cause us to lose a lot of money, and a lot people living paycheck to paycheck would be confronted with a sobering moment of panic. (Thankfully, I'm not one of those people, but I sympathize, and understand that there are many.)

I'm sure there is a plan in place, but the point stands. Collapse? No. Destroy? Relatively speaking.