You're thinking too big. "Normal size datacenters" is a small industrial building with 20 racks. And yes, they walk in, shut the power and start hauling drives. No joke.
> they walk in, shut the power and start hauling drives.
Or, if they suspect disk encryption, they don't shut the power. Instead, they dissect the power cords to add a special UPS, so that they can move servers without powering them off...