"Can the coach make a team better?" Yes. You can have all the best athletes in the world, but in my experience, it takes a coach to manage that team to bring out the best in the player, in the team. A great coach does not have to be a "my way or highway" type. A great coach is a motivator out of respect and appreciation. Not a "rah - rah" guy. But respect & understanding. Gets on your azz when needed, and can discuss it with you at the same time so you understand. And he has to have confidence. As a player, you want to feed off of that. And as a group (players and coach) it's all about the team to get to the ultimate goal. Win the ballgame at hand.
Personally, I would run through walls playing for coaches like Bob Stoops, Bill Belichek, Jeff Fisher, Tony Dungy, Dr. Tom Osborne. They all have what I consider to be great.