Because the earliest non military marching bands still emulated military bands in everything from music selection to drill standards. And US military uniforms for decades were influenced by European trends and things shakos were part of the uniform for nearly a century. Indeed they are still worn as part of the dress uniform by the Cadets at West Point.

While we can also track the influence of military uniforms on marching bands with other more modern trends, especially at the college level where many bands started as part of ROTC. The use of spats, and combination covers by schools like Ohio State or Penn State, or pith helmets like Rutgers are part of that same trend.