"I want to exit."
It depends what do you exit. Exit a computer window. To exit a building, a parking lot, a stage. To exit though the back door... You have zero context here, so it's not possible to consider it as unnatural.
They chose "exit" as the default suggestion, because it gives the general idea better than "to go out". It's easier to memorize and to picture in our heads.
"Go out" could make us wonder if it can be used in other situations. I see a little door with "to exit"....
Learning a language is also visual.