Your idea for NQS is... possible, but I'm not sure it's much my thing. I'll agree with the nearly-incorruptible, but she's not much of a leader, so you'd either need to have her grow in-fic, or claim that she has qualities that she's never demonstrated, and sometimes demonstrated actively not to have.
First, I'm definitely talking about manga Usagi, who actually experiences character growth. A couple more years and a few lesser threats under her belt, and she could become an effective leader. Her greatest ability as a leader is her ability to connect to people and raise morale, however, which is what these girls need, and when they hear that she was an actual princess in her prior life, it might give her a stronger following amongst the younger members. Being able to delegate well and using the aid of all of her Senshi as a ruling body for this society could lead to her becoming the leader you would not be horrified by the world accepting as Queen, even if the position had limited day-to-day effect on the various nations of the world.
As for why the dropping of nukes--it is the only event I can think of close enough to the time when those girls and boys started appearing that would make Japan unique. The effect could be spreading out from there, causing the next highest concentration of magical girls to be in the East coast of China and the other neighboring countries. A plotline that could be followed is that Japan initially tries to use this as proof of their genetic superiority, until it comes out that, percentage wise, gaijin born in the area are just as likely if not more likely to manifest supernatural powers.
On the other hand, if you want to go with them showing up all over the world and the number of them in Japan being a simple factor of population density, then all of the horrors of WWII could collectively be responsible. It could even be that the waning faith and belief in magic worldwide caused the available energies to concentrate in those who were most strongly attuned to it and most open to it, which were generally children.
Another possibility, based on the ley lines mentioned above, comes from the RPG Rifts. In it, a long time ago, Earth was one of the highest magic planets in the galaxy until an experiment performed by the most advanced civilization of the time, Atlantis, caused not only the destruction of Atlantis but caused most of the magical energy in the world to drain away. Since then, the energy had been slowly building back up, most of it staying contained in living beings and released upon their death to enter the lei lines and go into creating and sustaining new life. A series of nukes caused enough life energy to be released at once that the lei lines couldn't hold and dissipate it. This lead to fault lines slipping, setting off massive earthquakes and tsunamis, killing more people, dumping more energy into the lines, setting off volcanoes and massive storms, etc. What we are seeing in Japan in this fic is a small version of this, with the dumping of energy being enough to raise ambient magic in a local area.
An alternative take that ties in Sailor Moon is that Metallia and the war with the Silver Kingdom drained most of Earth's magical resources. Metallia could have broken out sooner, but it didn't want to because it would have starved. The actions of the early mahou shoujo and shonen, such as Sailor Moon and especially Tuxedo Kamen*, sped up energy build up in Japan, a spike which has slowly been spreading out over the planet.
*Given his direct connection to the life of the Earth.
Shadowrun also has an explanation, though it wouldn't work for why Japan is a focus for these events. In that, Earth is effectively in a magical tidal zone. We are at the end of the last low tide and the tide is rushing in, causing more and more magically active people to be born.
edit:
Maybe you should make a greater distinction between fantasy and reality then.
Just to clarify, I am quite aware of the difference between reality and fantasy. However, when the theme of your story is "How would the world react if it suddenly found out that magical girls were real, and how would they deal with learning of each other and their existence becoming public?", it is insulting to declare that the police and military would not only be useless, they wouldn't even try to help. A crackfic can be insulting to whomever it likes as that is part of the point, that it isn't trying to be realistic. The more realism you include in a story, the more offensive stereotypes and dismissals like this become. You may not find it offensive, but that does not make the multiple posters on here who found it offensive wrong.