I still don't get the apples to apples you think there is between football and baseball. We aren't talking about a coach wearing a faacsimile of a uniform that really isn't a uniform like you are talking about if a football coach were to wear a jersey and pants, we are talking about wearing the actual uniform. The point is wearing the actual uniform makes no sense in football, but it is a practical way to dress for a baseball coach.
As for the on field coaches in baseball, of course they aren't playing in the game, but they darn sure are active participants in the game unilike coaches in other sports. I don't see how you can't understand the distinction. In every other sport the coach is not on the field, and the coach has no influence on a play once the play begins. In baseball there are coaches actually on the field while the play is in progress, making decisions for team, reacting to the action, and directing his team to move and act as he instructs. There are no football coaches on the field telling Romo who to throw to, or telling Murray what hole to run to, but in baseball there are coaches on the field telling players what to do. Why is it so hard to believe that MLB might direct that any active participant on the field wear a uniform?
As for being active pregame, in football the players are the ones throwign the passes, running the routes, and kicking the ball, and the coach verbally gives direction. In baseball the coaches are throwing the batting practice, hitting the ground balls, hitting the fly balls, and doing so in 100 heat and doing it for 162 games a season. What you wear to do your job comes into play a lot more doing this over and over 162 times than it does 16 times.