Because it is an alternative history game. Germany didn't exist in this timeline either and you can form that.
See the green hat under my name? I've played the EU series before. I'm familiar with the concept.
Also, you could say alternate history until you are blue in the face, but it still won't change the fact that Paradox's handling of Japan's unique situation is inadequate. Its not entirely their fault, as development costs have to be spread on many different countries, and systems.
I'm just not satisfied with the portrayal of the Japanese situation. I'm not against alternate history.
That said, there are many ways we can suggest improvements to the current system, and with Paradox's DLC model it is entirely possible they will change/add dynamics to playing in Japan. You don't have to simulate history, or the Japanese political situation exactly, but you can approximate to make Japan fare more interesting. Why not have a Shogunal HRE system (yes, have Japan be 50-60 provinces) to determine who is Shogun? Why not try and simulate (via events, and decisions) the political/diplomatic realities (these guys were absolutely brutal, btw) of the Sengoku Jidai? Why not make it a struggle to remain Shogun after the war is over, and have the late-game be filled with trying to disarm your vassals? Why not have a system where the Emperor acts as the Pope, and you get tons of dynamic events from him?
You'd have to give it new tags for every possible clan (assuming you wanted a separate tag for them as shogun vs. them as random daimyo). One "Japan" tag avoids that. Anyway, while the shogunate is the shogunate, it still rules over a country called "Japan", much as we talk about "England" instead of "the Tudor Kingdom". Besides, the Tokugawa shogunate had far more power over its vassals than the HRE did over its members.
I understand the tag reason, but I still think its a rather bad system. Indeed, I think an HRE-like system is far better than a single unified country.
As far as Tokugawa control...I'm not sure if that's entirely correct. To be certain, they were not fighting against each-other after Ieyasu's assumption of power. That said, a potential reason for their uncontested control was the lack of external conflict. Japan isolated itself (sakoku), and did not face a foreign crisis until the mid-1800s. What is very clear is that in the face of a weak Shogun, the domains were very quick to retract their support.