On the other hand, an argument for uniforms would be that they remove a whole raft of problems with grey areas.

Without a uniform, you’d need to have a policy about ‘acceptable’ clothing - profanity, slogans, sun safety, workplace safety etc which would all be up to interpretation by students and an administration.
And you know that students would push the boundaries, and the ‘line’ would be constantly redrawn every week.
How short is too short on sleeves? What words are inappropriate on shirts?

Uniforms remove this - you’re either in the approved uniform, or you aren’t.