Just my own two cents, but perhaps a way of opening the games up for those who like more than just futa on futa would be nice? (The majority of futa games recently have been entirely futa only lately) Perhaps if some districts build up a certain level of infractions against the government they are required to have a female substitute one of their participants, thus removing half of their ability to impregnate others and lowering their chances of winning. Likewise some districts could attempt to cheat and enter traps/males in drag, thus making it impossible for them to get impregnated and causing a scandal for affecting the "purity" of the games. Etc.
I see your point... I can see several benefits and draw backs to adding more than just futa characters. A female contestant would be almost guaranteed to lose so there wouldn't be much insensitive to try in the games, even if they were one of the last two left they would have no way to make the opponent lose... unless a sponsor gave them some kind of cum injecting dildo? I would need to discuss it more.
I don't think a male getting into the games would be very likely, they would probably have tests to check gender, (from visual inspection to dna tests) they would have no way to lose if they did get in.
If more genders than futa are allowed, but I don't accept males, females or both into the games there are still roles they could play outside of the arena. They could be servants, interviewers, sponsors, stylists, fans or maybe even family of tributes.
What do you mean book-keeping? Like distribution of resources and management? I'm not sure what else that would mean