There is a line of thought, and I suppose it's not a completely meritless one, is that bringing something like a coffee to an interview signals to an interviewer that you are someone who is not prepared and doesn't delegate their time well.
And if you aren't prepared for an interview that you know is coming, how can you be ready for the inevitable unexpected developments in your job tasks?
Which I suppose is a good question... but that's something that would (hopefully) be revealed in the actual interview process, not because someone might have a dry throat and need something to wet the vocal chords.
At the end of the day, the origins of this "rule of etiquette" most likely stems from some dickhead with a lot of money who just didn't like the sound of someone drinking, and insisted people cater to his whims, and the rationalization for it followed later.