There’s already legal precedent for this under the Bald and Golden Eagle Protection Act. As far as I’m aware it’s illegal to keep them in the country without the express permission of the US Fish and Wildlife Service. Obviously they make exceptions all the time for non releasable individuals
The legal precedent is the Marine Mammal Protection Act. It gives facilities the ability to house these animals under special circumstances (display for education and research). Congress granted those facilities permission and they can take that permission away, which is the SWIMS Act. Obviously there are numerous laws and federal regulations dictating the captive housing of some animals, like the one you mentioned, and hopefully soon, the Big Cat Safety Act.