An interesting thread - because where I am, coaches have ZERO official input into game assignments, playoff or otherwise. Officials as a whole also have no official input.
For everything below the college level, local associations provide officials to various games, and the association sends the clients a bill. The client then pays the bill.
Certainly local assignors have an ongoing dialogue with coaches, AD's, etc., but playoff and provincial championship assignments are made by a committee of senior officials and/or local executive officers.
Our system must seem downright dictatorial to you folks