SNAA: I've served on the board and helped raise funds for several youth soccer clubs. I've actually seen clubs faced with the issue you raised. I thought I'd respectfully give you another perspective.
A vocal parent complains about a kid's playing time. The parent gets other parents on the team, or the board, to fire the coach. It's actually in many clubs not that hard - parents whose kids are getting a lot of playing time and even many who aren't are not focused on youth soccer so a vocal minority can be raised pretty quickly.
The coaches, no dummies they, notice. So do the parents who have complaints. The coaches tend to start biasing playing time toward the kids with the loudest parents. More vocal parents tend to gravitate toward the more authoritative positions (the board) and make more noise. The coaches notice more and make sure those kids whose parents who are vocal, and particularly board members, get playing time. And the cycle deepens.
This is the essence of a "political" club.
There are people out there who do not wish to be in a political club. Those people gravitate toward clubs that are professionally managed.