Asking the primary professor of your target grad school to review your statement of purpose
Your hunch is correct.  It would not be ethical.

However, if you have a mentor in your current institution, you can certainly send this person a link to the primary professor's home page, and your essay, asking for feedback.

But before you do, here's a pretty effective exercise.  Imagine that the trusted mentor is reading your essay and jotting down comments in the margin, slashing here, asking for more detail there.