That's why you advertise all prefixes on the foreign media. Suppose the prefix indicates that the foreign agent is on the same network. But then you still have to do the same work, to determine that the old foreign agent is gone, and register. I consider this to be a benefit. Suppose the mobile client is wired, and moves from one network to another.
Wiring is irrelevant.
Ignore for now the problem mentioned above about several subnets on the same wire.