That's nothing a rack full of fast switches can't handle. A rack full of fast switches already does handle it - where do you think the original copy came from?
They will get a copy of the whole feed, but not store all of it - they will have heuristics for selecting interesting traffic.
Switches handle data at far faster rate than any hardware can actually inspect it, store it, process it, etc.
But yeah, just a rack of "fast switches" is all it takes to route hundreds of petabytes of data each day. You should let the data center operators know. They'd save billions.
Switches do inspect it. They also have a feature designed for wiretapping, which copies a percentage of traffic to another port. They may have a feature to copy 100% of traffic matching a certain filter. Managed switch ASICs have this feature even though it's usually not exposed in the CLI.
They will get a copy of the whole feed, but not store all of it - they will have heuristics for selecting interesting traffic.