Do you think Red was the key? Or possibly Russell, Cousy, Havlicek and Jones etc etc...
Think NBA coaches are tremendously over rated, NFL less so, but still not the determining factors they are made out to be. Yes, again you can't survive an incompetent one, but everything above competent is fine.
In cricket, great players makes great teams... There's a thread ongoing for an AT SA XI where I believe Graeme is going to easily gain the captaincy nod. A few months ago I asked if he was even a good captain, to which there seemed to be no consensus answer. There's also no consensus answer as to what makes a captain great.
Wins / losses
Man management / instilling discipline
Tactical acumen
A combination of all 3?
A team doesn't need a great captain to be great, it requires quite a bit (that I wouldn't get into right now), but a great captain isn't one of them. A great team (or performances) however, does tend to make us see a captain as being great.
AB was a great captain, he instilled the discipline, was great tactically and he turned the team and culture around, but it wasn't until the quality of players improved, that the results (especially for subsequent, and possibly lesser captains), reflected it.