Same reason why Ibuki's boss forbid Solo sensei asking an assistance to the school. The system ain't that broke yet, so don't need to fix it. It's only problematic for now because its exclusive to this mission.
Heh so Prince Wakamiya openly said wanting to take a business trip for 3 days was for this exact reason.
To make the courts took the bait and issued an emergency meeting without him and crowning the other one.
Probably in part 3? Just a quick auto translate on twitter, author said already have some inspiration for the next part. But probably not in the near future as its doujinshi. Probably this late year or next Jan.