Hmm, yes, you are right of course. I had to think about that! Pointing the needle to 360 just means it's ahead of you and you will start a spiral downwind but always facing straight towards the beacon. So that is not equivalent to keeping a lighthouse on a constant compass bearing.
But if you offset your course, into the wind, to keep it on the same absolute bearing then you will fly straight down its 'radial'. Don't I achieve that if I adjust my course into the wind so that a steady compass course keeps a steady relative bearing, which will not be 0/360?
OK, maybe a VOR is easier!