Harsh perhaps, but completely honest.
The OP's situation is no different from work, where a group head is called to make decisions that aren't popular with everyone in the department, where highly competitive persons and egos abound.
Situations like this separate great leaders from good ones.
OP's situation is completely different from work-for-hire.
Leading workers and leading volunteers are two separate things. If you are leading paid workers, you do not have to spoon feed them information and beg them to show up. Paid workers have far less freedom to leave at the drop of a hat, for a variety of reasons I probably don't need to list.
I mean, think about it. Does the head nurse have to call the subordinate nurse to make sure she will be there on time for the heart bypass surgery? Does she have to give her the address and plead with her not to show up at the last second and allow time for traffic, and then thank her repeatedly for doing these basic things? I have to do all of these things.
When you're the boss in the workplace, your subordinates work for you. When you are the captain of a tennis team, you work for your teammates.
Also, it is naive to suggest that the captain give up her playing spot because a player gripes about not playing. The captain's loyalty should be to the team, not the squeaky wheel. And if it is doubles, you have to consider the preferences of the partner, who might not wish to play with Squeaky.
You probably have more workplace managerial experience than I do. I think if you were to try to lead a tennis team the way you would run a successful business, it would make for a great sit-com.
I can see it now: "Karen, you're playing No. 1 doubles with Missy, 9 pm, East Side Courts."
"WHAAAAT? Why am I Doubles 1? Becky and Sara should be Doubles 1! I didn't join this team to be sacrificed! Besides, I told you Missy and I don't do well because she's a head case! And no way am I playing a 9 pm match! I won't get home until midnight, and I have to get up with the baby in the middle of the night and get my kids off to school. Nah, that won't work for me."
Good luck with that.