Leave X can mean exit the area X, but it can also mean to go/stay away from X.
While X is usually a place, or a person, it can also be a smaller item or object.
So it implies walking away and getting a significant distance from X when X is a place, but if X is a small item then the distance can be short, especially if you tell someone to leave it there or leave it on the desk (example).
Leave can also be used like this:
- leave X alone = ignore X
- leave X be = stop bothering X
- leave X out = don't put X away
- leave X Y = don't change X's state from Y
The student may be allowed to have the phone for emergencies, and thus need to see it, but the teacher simply doesn't want the student doing anything with it.
- Commands with fewer words are less polite and more demanding sounding, so leave X without the last word may be something you say firmly to someone who is being difficult and should know what you mean. But then you might want to tack on a "please" at the end so you don't sound too harsh.
So it's not unreasonable to use leave in the way it's used in your question.