It's not entirely true there's nothing of the characters in the film, just the stuff cited is a bit more of it.
The male computer voice is an actual voice filtered, not a Hawking type voice. And maybe it's deliberately designed to sound that way to cut through the actual human/alien voices in an emergency. When that voice comes on, you know it's the ship saying, "Yo. Problem!"
Posssible, but the voice (Majel) used in the original series WAS distinctive and any crewmember hearing it would know the they were hearing the ship's "voice" and to pay attention.
Really if the old "Majel voice" had said, "Emergency alert--negative control at helm!"
....would anybody there NOT have understood who/what was talking?
Besides just have Sulu or Ilia say it.