Yes the transactions couldn't be just copy-pasted on B, since the whole point would be to change into a different signature.

On the purpose on keeping Bitcoin-A, it would be for being conservative regarding such change into B. Ofc A would still be a hard-fork from the original, and users would still be required to keep keys from both A and B in order to just use A, but oh well. I'd say it's for the sake of not jumping entirely into B, or to still keep having one feet at A. 

I think this is the closest to having a B as backup while being as inertial as possible on the original.