From a TV context, it would have looked boring with everyone in the same costume. Only Picard & Riker wore a 'standard' without some accessories. Data was yellow, Geordi has his VISOR, etc. Even that changed with Picard's 'casual wear'. What struck me as funny was when I met Marina Sirtis in person at a convention during TNG's run, it was obvious that the costume was actually not flattering to her. It was a rare case of seeing a TV actor in person and going "Wow! They are so much better looking than on the show!" And she didn't look bad in any of those silly wardrobe choices.
But it is fun to create a reason why, isn't it. And yeah, Riker was the 3rd boob.