Man, that escalated. Surprising, but also not.
So I understand the bloodlust you've all got, but you have to understand that what she did was a potentially Major MAJOR Problem. Like we're talking 'Could get them both killed' level of problem. We're talking 'Could Literally start a Civil War' level of problem. See, and admittedly what I'm referencing comes from the history of the Eastern Roman Empire but I'm going to assume that similar things happened in Imperial China and even if they didn't the Manga suggests that a similar situation exists in their fictional Empire, Sports, especially Team Sports, are massively important. In particular, backing a specific team can be, for a politician, less about team loyalty or love of the sport as we would understand it and more like a Political Statement. Some historians even go so far as to suggest that the Byzantine's Blue and Green Teams were comparable to modern Political Parties.
The Manga does explicitly state that the North and South teams are extremely competitive, and showing favor to one team is almost assuredly an unofficial way for politicians to make statements of who and what they support. Given the description of the soldiers of the North Branch as 'Snobbish' they are probably tightly connected to the Nobility. Likely this would have been explained to her in the lectures she stopped paying attention to. For the Emperor or Empress to show favor to one team or another could seriously compromise their standing with the other team and thus compromise their standing with the Nobles and Politicians that support that team. And by "Show Favor" I mean the comparatively simple and easy act of even complementing one of the participants in public. For the Empress to actually take part in the games on a specific team's side would not only be a major faux-pas but is all but declaring "The Emperor has decided that this is the only team he cares about everyone else should go fuck themselves", even if he didn't even know about it let alone order it.
For Reference, the
Nika Riots of Justinian started with mounting taxes against the nobility causing discontent, challenges to legitimacy due to a not particularly spectacular war, and anger from a remarkably balanced legal decision.
The Nika Riots ended with 5 days of Riots burning down much of the city including the Hagia Sophia, an actual literal attempted Coup against the Emperor that went so far as to bring in a new candidate and literally Crown Him as Emperor, and 30000 Dead.