Before you read this and say this is some clickbait, I will tell you that this method doesn't work for all game modes. It works for more than half of them though.
What you have to do to get the default assistant coach instead of that generic douchebag is to start the game neutral, just as you would want to see a CPU vs CPU matchup. During the jersey selection screen, before you hit the button to start the game, you shouldn't be controlling any teams; keep the selection logo in the middle.
After the game has started, the teams default assistant coach will load and suddenly the douchy assistant coach is out of the picture for both teams. Before the tipoff, you can go to the main menu- choose sides, and select whatever team you desire and the teams will still have the real assistant coaches on their benches. During timeouts we finally can relax and make changes without that motivational guy screaming at us. Silence is beautiful. The user players will just move their lips while on the bench, "talking" to the real assistant coach without their voices being heard, just like in real life.
This works for exhibition/Nba today matches. IMPORTANT: Even though you choose the team you want to control before the tipoff and therefore before any second of the game has passed, 2k sees this as cheating and team switching. That means no achievements for you during that specific game. If you care about the steam /xbox one/ ps4 achievements, after you are done with choosing the team you want, go to main menu - quit, and select rematch. Don't worry, the real assistant coaches are still there, no sight of the douchy screamer. You will know control the team you want at the start of the game and still be able to get achievements.
This should also work for MyLeague and playoff mode if you do the settings right. Even though in myleague for example you want to stick with one single team for the entire season, during the league setup you can choose to control all teams.(controlling doesn't mean you have to manage all the lineups and so on, it gives you the possibilty to choose sides during myleague games, so don't worry about being overwhelmed). This will allow you to do the trick from above. The same goes for playoffs mode.
I don't think this method works for game modes like MyGM, MyCareer and MyTeam because you are pretty much locked in on a single team, you don't have the option to choose sides and stay neutral.
This is how my timeouts looked like while controlling the Hawks:
This + music arena and commentary in the background, no coach voices heard.