I get what you’re saying and certainly accept that the precedent might be set. Saying “36” over radio is certainly less ambiguous than “00”. For the visual display, however, my opinion is that 0 is better than 360. But that is just me 
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One point to make though is that a circle is counted from 0 to 360 (or 259.9999999…), not 1 to 360. Otherwise how do you describe a wind direction that is 0.1 degrees east of north? 360.1 has to wrap to 0.1.