This may be the way SirusXM works, but it is far from optimal. The best scheme is to give the radios simple sequential (or near sequential) id's, and have the station transmit a bitmap of which id's are enabled/disabled. Then it's one bit per subscriber, and can be transmitted in a few seconds. That bitmap is authenticated by a public key stored in the radio. You might want to run length encode the bitmap if you assume that in 30 years there might still be a handful of ancient radios still alive you wish to service.

Satellite bandwidth is expensive... Activation time is annoying for customers... The above scheme saves either (or both).