i've never understood coaches wearing uniforms.
I think Connie Mack was the last (and only??) manager to wear a dress suit rather than a uniform.
A guess: early in the 20th century, MLB rosters were looser, and a coach might be sent into a game if a player got hurt. Go through Baseball Ref for the career of Clark Griffith's pal and Washington coach / pitcher, Nick Altrock.
That's just a guess...but if it was done in 1912, there is no reason to change in 2012.
Biggest changes I can think of: much larger gloves, batting helmets, and that disgrace of 1972 (?), the DH. Artificial turf, but most of those ballparks are gone, thankfully.