Definately a loaded question and I doubt anyones gonna answer it as it was asked.
My take as a Head coach, assistant coach and as a parent is that it definately takes a staff. Coaches need to have a role(s) and understand what they do well and bring that to the table.
Head coach needs to be a leader in all aspects. He/she needs to communicate well with the coaches, parents, umps, and most importantly the players. Be consistent in the approach, do what you say your gonna do. HC needs to understand what they themselves do well and delegate responsiblities to hopefully knowledgable assistant coaches, know when to admit they dont have the answer and always continue to be a student of the game and create students of the game! Needs to have consistent accountabilities for players, coaches, even parents. We are in this together and HC needs to try and keep everyone as engaged in the process as possible....roles!
If possible, they should have coaches that know atleast as much or more about the game, atleast in some aspects, and teach that part to the players and be thier "go to" on the subject, fielding, hitting, pitching, whatever. Having a staff of coaches that all have the same medium level of knowledge and/or yes men does not do much in getting a team better. HC has to be able to trust the assistants, but be able to call BS and make the ultimate decisions.
Lets be honest, softball is not rocket science, but there is alot more than the 90-95% you see coached. Most coaches and even parents can take talent and win 90% of the games or manage them. The trick is finding coaches that can get that last 5-10%. Things like motivating players, truly teach the game by being able to break down the fundamentals, handling adversity or success evenly, the various mental aspects of the game, can they coach in a tight game managing the clock, dp/flex, sub rules, lineups set up to score in bunches, yet also able to manufacture that timely run. The softball chess match we see played out every weekend. Etc....
Things I would look for is, can the coach or staff continue to instill that passion for the game my DD loves? Can they make her a better player and more importantly a better person? Do they understand what she does well and recognize where that fits into the current team. Have they taken the time to truly get to know her, what motivates her, what her goals in softball are and can they help get her there. Get down to their level and show that compassion that young ladies need to feel to be successfull. The old adage, "girls need to feel good to play good and boys need to play good to feel good", is very much real. I always like compliment-critizism-compliment ratio.
I know I hope the young ladies that I have had the privilege to coach, feel like I had a positive impact in their development as players and young ladies. I make a point to try and stay in touch and see how they are doing, even when on another team. Coaches need to really care about the players beyond just as little robots to win games with.
There is no silver bullet. No perfect coach. Every player and parent has different things they look to or respond to. Life is full of trade offs.
My 2 cents....
P.S. Before my phone blows up, this posting is just my opinion and certainly not directed at current situation or past. We are very happy with our current HC.