Nice thread Sue.
Well here, it is the opposite. Good coaches are hard to find. So, they tend to put the blame on the player when he gets poor results. They are the choosy ones.
From personal experience, my son has been with his coach ever since he started palying except for a very short period. Two years ago, he had a nasty fight with him and decided to change him. As he is the one playing, I don't interfere with his decisions. He was mad because he thought his coach didn't pay much attention to his weak points and thought he was not helping him enough overcome them. He stayed with another coach for 5 months (one of the best available, considered even better than his own coach) and his level really took a dive. There was no chemistry (another important factor) between them and they never liked each other. He was too proud to go back to his old coach.
Fortunately for him, after seeing his results, his old coach gave him a call and asked him if he wanted them to work back together. My son accepted immediately and they've been together ever since. Because he is young and not yet on a "professional" level, he is very emotionally attached to his coach. He looks up to him as a big brother and will not hear of changing him.
The point is, when you are a professional and can afford it, if your coach isn't giving you the results you are looking for, you will most probably change him. I think most players are mature enough to know and evaluate where the responsibilities lie. If they keep kidding themselves that their results, or lack of them, are solely the responsibility of their coach, they will never reach the level they are aiming for, even if the coach plays instead of them.