It's counter to what sci-fi taught us using AI would be like. We never thought we'd have to feed it words of encouragement, we expected it to act more mechanically, like the computer interfaces we have been using, but here we are. It's kind of quaint, and kind of endearing.

Been watching the wrong sci-fi :). Star Trek had both AI modes as primary characters, in form of the ship's computer, and Data (TNG) / the Doctor (VOY). LLMs are actually great at acting as both, but I don't believe people thought much about what is required to make the "simpler" interaction mode of the ship's computer to work.

Or what would make automatic doors work like on Star Trek and not in real life.

The answer is: the system must obviously see much more than your prompt. It must have continuous awareness of you and what you're doing, so it can understand intent behind your short request (or action, like approaching the doors vs. passing by them) and "do what you mean" instead of act like regular computers today.