All (european style) football managers/coaches who want to be taken seriously wear a suit, or at least slacks and a shirt (two examples out of many, many more).
As do most of them in hockey. And I think (from my limited experience) that most of them in the NBA wear suits as well.
But why don’t american football ones? And why do the baseball ones wear the match dress?
Just a minor squibble that’s been on my mind for a while now.
The NFL has (or had, I’m still googling) a dress code that requires the coaches to wear Officially Licensed Merchandise[sup]TM[/sup] with their team logo.
Here’s a link to a news item from 2007, about Mike Nolan (coach of the 49ers) getting the rule changed to allow him to wear a suit. This being the NFL, it has to be an officially licensed suit.
Baseball probably has it’s roots in the playing manager days.Football does not have that heritage . Old hockey days had the trainer come in for an injured goalie. I see them wearing a uni.
Connie Mack wore a suit in the dugout, but it’s possible he didn’t go on the field, letting coaches talk to the pitcher. Either that, or he was grandfathered in.
Connie Mack wore a suit and tie during games, but he had to stay in the dugout- if he needed to communicate with a player on the field, he sent a uniform-wearing assistant coach out to convey his message.
Going back to the OP’s question, American football coaches tend to run around a lot on the sidelines, not like football managers who sit pretty much the entire match except to yell at the referees. In baseball, as noted above, it’s just the (ridiculous) rule that managers wear uniforms.
(Professional) basketball coaches do generally wear suits during games, for the record.