Speaking of Data, his existence anywhere near that ship's bridge is a humongous breach of all sorts of security to begin with. He's a not-very-well-understood piece of tech that's been proven to have at least one hidden backdoor into his brains that can let others assume direct control over him and use him to do some exteremely dangerous things. Letting him into the bridge of such an important ship and giving him such high clearance is just insane.

But of course why worry about Data given the captain himself and his history with the Borg. In other words it's Star Trek, so whatever. The show must go on.

It’s not exclusively a voice print. The Computer also has a verified identity chain for the person speaking — it is aware of where everyone on the ship is and who they are, against a manifest, at all times.

Or unless it's anyone with a tape recorder

Cyril would end up on a Cerritos grade ship or a garbage scow. And Pam would be head of security

Yes, easily foiled with recording equipment (See: Archer), but recording equipment has a weird almost Schroedinger's Cat-like status in Trek...