I agree with the gist of what defy said earlier.
I was pretty excited to coach in newbie mixes after being asked to by its organizers but after a few mixes I quickly lost my appetite for coaching. I was only interested in playing as a medic in the mixes because I feel it gives me the best ability to teach and guide with minimal "dm-influence" on the outcomes of the fighting. These concepts I'm gonna talk about seem so basic and obvious but it looks like most people don't get it or don't care. Both mixes I played in I had to face the coach on the enemy team playing demoman on badlands while I was the medic for my team. It was absolutely crushing. Their demoman destroyed everything since he was way better than our, actually newbie, demoman. There was very little for me to teach my team outside of some setup and questions in pre-game. Once the game got started the main takeaway was that "hey, their coach is like 40x better than our average skill level on this team and is carrying the shit out of them while our coach can't really help since he's medic". I suppose I could try to stay positive but it wasn't my negativity that made things sour. My newbies were getting pretty bitter on their own, and they were right. Other coach would spearhead pushes and peeks, get two or three picks, and then direct his team to overrun us. I'm really wondering what the comms in their mumble were like and what they were learning. Maybe they were learning some good things like when to push and how to go together, but is it worth potentially ruining the impression of the game for 5 people to give 5 other people the simple joy of getting carried? There's a lot of people who, at least as far as skills vs newbies go, don't have a not-main-class. There's plenty of people who are, say, a high-IM scout that also translate to a low-IM demoman. What is even the purpose of this distinction in this setting when the coaches are trying to crush as hard as possible?
Now let's say I was playing demoman to counter the other coach. This inevitably becomes a dick measuring contest of minimal benefit to the newbies. I do not feel like I would be a very good coach from this position since I would be focusing a lot of my attention on either A) killing as many enemy newbies as I can to keep my team in an advantageous position, or B) shutting down their coach to keep him from doing the same things unto us. Perhaps I'll play an offclass such as scout who I'm extra-bad with and have litte experience. Again, I find that I'm going to be using my mental resources to manage my unfamiliar circumstances and make sure I'm pulling my weight, or carry rather than coach. I find it difficult, and maybe even a little bit dishonest, to play without trying really hard to win. This is particularly true when the coach on the other team is clearly carrying them as hard and fast as he can. These are non-issues if the coaches are PLAYING MEDIC where playing your hardest is actually a good thing. If someone says of themselves that they're bad at medic and therefore can't play it while coaching then they probably shouldn't be coaching newbie mixes. "But what about all the medic newbies that want to play?" Honestly, they can just spec the coach. Of course playing is better than watching, but at least it's live and engaging and they can ask questions. But there's an even better way: The way it used to be done. Put the coaches into spectator and have them guide their teams from above. I've seen newbie mixes from long ago done this way and they seemed really good. I can't for the life of me understand why this method was abandoned.
TL;DR - Coaches too often dm-carry their teams instead of actually working with their newbies. Coaches should have to play medic, or (even better) be a spectator and guide their teams without being on the field with them.
Shoutout to pie_hero. I've watching him coach and he's so damn good and professional, it's heartwarming. Kudos to you!