Perhaps there might be some reason to identify the biological origin of the 'signer' to show that the Talosian illusions didn't only affect humans. Any other "in-universe" ideas why this might be done?
Perhaps Vulcan wasn't yet in the Federation , so that some relevance might be attached to his service origin, the way that (hypothetically; I have no idea whether they would ever do this) Allied reports might refer to a member of the Lafayette Escadrille as American Pilot (Name).
 Yes, I'm aware that at the time of production, Earth wasn't yet in the Federation either. I still think the cross-service idea is the least problematic one on hand.
Vulcan is a founding Federation member. It has always been in it.