I think this problem is related to several factors:
First of all, in the top competition, the coach seems to only have sportswear and formal clothes to choose from, and casual clothes will appear out of place.
Normally in a formal occasion, whether it is a meeting, a game, or an interview. Suits are often the best choice. It can make your whole person very serious and formal. No compromises on these big occasions. Therefore, in top games, most coaches will choose to wear suits.
Coaches in suits will be more eye-catching on the sidelines (especially football), which is convenient for command and camera capture, which is an important factor.
There are rules about coaches wearing suits, just like players have to wear tracksuits. In the case of this kind of game, the coach has to be distinguished from the players. Therefore, as a coach, you need to wear a suit to adorn and differentiate. Including during the game, for the camera capture, the cameraman can distinguish between the players and the coach, which is used for cutting shots.
Except for "clothes racks" such as Loew and Mourinho who maintain a good figure, most of the famous coaches have gained weight, and suits can cover up their shortcomings better than sportswear;
The coaches are generally senior, and there are more or less senior coaches. Suits can modify their figure. Photogenic will be more self-cultivation and solemn formal.
However, there are some coaches who don’t like the sponsor’s brand, but they cannot wear sportswear of other brands due to contract restrictions, and suits have no logo; in addition, suits are more solemn and authoritative than sportswear, so it is natural for them to become the first choice of coaches of.