This was made as such the case by his former agent and longtime Russian friend Sergei Fedotov. He talked on the Russian language podcast Bettman Will Call not too long ago. Quotes were transcribed by sports.ru and are translated via Google Translate.
"“I have known Zhenya (Kuzy’s Russian nickname) for a very long time and are friends. There are people who are quite disciplined. Zhenya is not in this category. Zhenya from the category is closer to me… if I don’t feel [inspired] from what I do, I will definitely look for opportunities to make me feel comfortable. It is an inner and mental state. Right now, Zhenya doesn’t have this [joy] from hockey, and Kuznetsov, without this recharge, without a spark, he’s not interested in anything. He wanted to change the team for a long time, he was tired in Washington, and also – not only aggravated, but in many respects it was influenced by the fact that Laviolette does not play the hockey that is typical for Evgeny Kuznetsov.”"
It is an awkward breakup indeed. The only way he could be around is if Kuznetsov likes the choice for the next head coaching candidate. But maybe this quote by his former agent indicates that the damage could’ve already been done.
We’ll always have 2018 playoff Kuzy to remember, cherish and thank. The Barry Trotz style was much different and maybe Kuzy and him got along. I don’t remember Trotz having issues with Kuzy.
Now maybe Laviolette wasn’t a good hire. It’s important whatever Kuznetsov decides to do that the team hires the right coach so none of this happens with anybody else.