I've had two different trainers tell me I should put a running martingale on Excel, but I won't do it. At times, he can become somewhat high-headed in new surroundings, but in no way is it dangerous or even an act of resistance. He does it to take in his surroundings, and after warming up will bring it right back to where it needs to be. I won't use a martingale because it's something I can easily work through without needing to rely on it.
Yes, there is a time and a place for standing, running, German, etc. martingales, but if you don't think you need it, there's your answer.