It all depends. Coaching absolutely matters in terms of player performance. I've seen it time and time again no matter the sport that the same team with different coaches performs differently. For me one of the key attributes to coaching is not individual performance but getting your team to play together and identifying and utilizing the strengths of the cohesive unit. And not that it should be like this at the professional level but being able to motivate each player is on the coach to enhance as well. So yeah if players don't play well sometimes it's on the coach.
Coaches tenure are not well secured, not even in any league. You might bring your team into a championship and win. But if in the next season the team fail, the thing one who are going to take the blame is the coach himself. So I'm not surprised by it, I'm not saying that it is a practice, but usually that's what is happening in any league. First, they are the leader, they are the one who bring this player into unison and just focus on one goal and that is winning. If he fails then the management will have to find a new one as the players are not responding to him. Second, if ever he brings the team into a champion, and then the next year he failed, then his system is no longer working and maybe the management will also find him liable so he will get sacked despite what he brings into the table the previous year.