The internet is not magic.

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Of all the bullshit and misinformation you get about the internet
>Oh its a cloud
>Everyone is connected
The facts are simple there are a handful of backbone equipment that rout everything imagine a simplified (without the cluster we have today) (also good luck on finding where these parts actually are, pro tip its a secret) version where you have a ring around the USA and all 4 nodes are connected. Everyone is hucked up to one of these 4 nodes and they push your trafficker to the other backbone nodes.

Sniff on these nodes and you know what is going on.
There is no more magic.
Also if you cut the connection between the backbones you effectively isolate a network.
Since our example is a 4 node ring you need to cut 2 cables to create total isolation.
Now the new sub networks will still operate and communicate however considering how the modern web requires multiple requests chances are your favorite websites will not be operational or not on your new network.

This is the simple truth.
It gets more messy and complicated if you see the diagram however the same concept is observed.