I can only speak for Nashville fans. Yes, it was a big mistake by the Caps letting a Cup winning coach go like that.
I was in Washington DC on June 20, 2018, the day of the Stanley Cup celebration. I went to visit the Smithsonian that day. I always wanted to go to the Air & Space Museum and also visited at the American History Museum. I was on the National Mall with about 50,000 Caps fans.
I saw Barry Trotz, the former Nashville HC of 16 years speak from 100 feet away. He gave a VERY STRANGE speech. I thought he must have been up all night and drinking too much. I was more surprised by what he didn't say, than what he did say, like we will be back next season for another Cup. A week later, he was HC of the Islanders. I was quite surprised.