It will always and forever be a problem until coaches are removed from the assignment process. Maybe maintain a way for them to scratch, but they should absolutely not be selecting individuals and/or whole crews, and maybe not even chapters.
Unless there is some sordid conspiracy that gets brought to light that materially affects the integrity of the game, it will never happen though. I've had a LOT of discussions with various personnel, on both the officiating and coaching/staff side, and here's how I think this could be done:
UIL has responsibility for picking chapters for certain games (probably area or quarters and above, based on availability and location of the mutually-agreed upon site.)
UIL assigns chapters for particular games, period. If a coach wants to scratch the assigned crew, fine, they get one entire crew scratch (not person) per round, 2 per post-season - but it is assignor's choice, based on chapter methodology for selection, not coaches' choice, for the second crew. (This would minimize the possibility of a 'buddy-buddy relationship between a coach and crew, since the other coach could request different officials.) Coaches can appeal a chapter assignment only if both coaches are in agreement, and UIL is absolutely not obligated to make a new selection (depending on the arguments of the coaches as to why that particular chapter shouldn't call their game.)
Each chapter is responsible for having a published prioritization/qualification system to determine what crew, or individual personnel, if the chapter doesn't use crews), are qualified for postseason assignments. This will help reduce the perennial problem of internal gritching about who did/did not get certain games inside the chapter - you want those games, get qualified for them. (not a perfect solution, but better than current, IMO)
And here's the real pickle that gets everyone worked up every year: championship games.
For state championship games, UIL will publish a schedule at the beginning of the year, based on rotations, that assign a particular chapter to a particular championship game. I have heard the argument that 'we just don't know if Chapter X or Chapter Y has enough quality officials to officiate a championship game, so it should always go to a major metro chapter' and it is arrogant and ludicrous. EVERY chapter in the state is capable of producing a championship-quality crew. Every single one, not just major metro areas. Yes, there are more chapters than championship games - every so often, you're the odd man out. This may not be a perfect system, but it as hell is better than what is in place now. And no, it doesn't eliminate the internal politicking and jockeying for post season assignments, but having those criteria established at the chapter level, will help with that. At least it minimizes the (VALID) complaints about chapters being completely overlooked based on incorrect, ignorant assumptions about smaller, rural chapters.
//steps off soapbox, carry on//