why do u.s. postal letter carriers have a blue strip on their postal trousers ?

Answer 1

Because it's fashionable.

Answer 2

The stripe brings together the different colors of the uniform in a professional, neat, and yes, fashionable way. Since the pants are blue/grey, the shirt light blue, and the shoes are black the blue stripe helps create a clean line connecting all the elements.

Now if you want a real brain bender consider why we wear uniforms at all?