Plenty of reasons, but let's focus on one that will pay off immediately when players are very young and continue through their careers.
Run when they run and play the game with them.
The team includes the coaches and by participating in practices you'll make a connection. Standing on the field barking out instructions gets old fast and the players sense a disconnect from what you're asking and what they are doing. "Why do we need to do it if you don't?" is what some players are asking themselves. Some coaches may seem offended because the "coach" is the authority figure. You are, but you're not a dictator. You're a teacher and you need to establish trust.
Some coaches can't physically run with the speed and endurance of their players or even play the game well. Learn with them. This is a way to understand how the instructions and drills you're endorsing apply to the game conditions. Better yet, you'll become the entertainment of the practices when you mess it up or crash and burn. Remember, you're the parent that is on the field playing the game and putting the time into the team. The team concept succeeds and fails together and this includes you as the coach. Many of the best memories my teams likely have are from practices as we laughed, worked hard, and learned how to play the game with a focus on fun. I've been the entertainment with our coaches along with working as hard as anyone.
One of the great outcomes of a practice is a unified group that just worked through something together. Everyone will enjoy practice more and learn, including the coaches. After a few seasons of it, it'll seem weird if a coach doesn't get engaged as you did. One of my favorite phrases to hear is, "coach, STOP covering me so much. You're messing me up". If that player can break away from someone bigger, they will have success against their peers.
Don't forget to warm up, and stretch too...You aren't as ready for it.