Yeah about 6 months into brown belt I had to switch gyms to a gym where the head coach was a pro MMA fighter and ADCC vet and it leveled up my game so much. He had all of those attributes that you mention and also had a culture of that instilled in even his lowest belts, and even his newer guys made you feel like you were in much more of a "fight" than every other "BJJ academy" I had ever been in. This was an MMA gym through and through that just happened to have jiu-jitsu classes.It's not necessary, but it's very useful. Only because dealing with someone who knows how to strike from the top while maintaining position and mixing in passing is very different than dealing with your gym buddies who don't know how to strike on the ground at all. Generally speaking I think training with MMA fighters is good for anyone's BJJ, because they tend to be in great shape, they don't consent to play the normal BJJ meta-game (you have to spend a lot of energy just keeping them down), their games tend to be wrestling heavy, and they won't tap unless you really, really catch them. It tightens everything up to train with guys like that.
Just rolling with people that will never concede a sweep to play guard and actually force you to hold them down effectively after sweeping them? Or needing to finish a sweep by coming onto the feet and getting a takedown? Or taking a month to not play guard but stand up anytime you get taken down or swept? Those 3 things alone improved my overall jiu-jitsu so fucking much.