I speak to the public. I am speaking in public. It doesn't seem grammatically correct at all
I am speaking "in public" . I am speaking "out in the open." We don't say, 'I am speaking "out in open."
Speaking in public is correct English seemingly, but it doesn't come across as being so (correct) upon further scrutiny. Kindly dissuade me from my conclusion, for which I personally have no resolution.