I've never seen a separate plate for bike racks. Technically in many US states, a bike rack could get you pulled over for having a blocked plate but in practice police don't enforce that. The assumption is the front plant is enough but then not all states require a front plate.

The license plate and registration laws in the US are very fragmented. Some states out the registration on the license plate, some on the front or side window, and some are moving to digital only registration.

Essentially with almost no work, you can make proving you don't have a validate plate or registration difficult. You can just print a fake temp tag (paper license plate dealerships use) for a state like Texas but drive around in any other state since they have no way of knowing it's a fake temp/dealer plate.