The Japanese can't lose the Zero because it is a crucial part of what Firaxis is portraying with them, namely their involvement in WW2. With ideologies being such a prominent aspect of the game now this is more important than ever. Japan needs to be able to adopt autocracy and attempt to conquer the world with this unique unit, same as how the Panzer is a crucial unit for the German empire for the same reason. The Zero most likely needs a boost because while its special ability is powerful it is too situational, but it shouldn't be replaced.
Japan already has kamikaze - it's called Bushido. Bushido precisely encourages a kamikaze style of play. If you gave them a unique building instead it would dillute their role as a warmonger civ by making them builders and lessen the impact of their unique ability and whole role in the game. Japan is not a builder civ or a cultural civ, they're isolationist, and they're warriors. That means Japan needs to be a double unique unit civ, making a tea house a strict no-go. Besides, the tea house is already symbolized in the game in the form of the Bushido ability in that these two are both about Japanese tradition for and concept of 'Honor' - but it is better reflected by the unique ability than by a would-be unique building. Japan is perfect as is.
I do agree that Japan needs a hand, but that needs to come in the form of Firaxis stopping to put all these insane roadblocks in front of warmonger civs, not changing Japan as is. As was noted above, there are too many penalties for warmongering - that is Japan's real problem. The Civ 5 diplomacy is borked as a whole (with diplomacy revolving almost exclusively around this 'warmonger hate' that seems to just never subside, even hundreds of turns later) and I don't see Firaxis fixing it, but the simple change of making warmonger hate drop much, much faster than it does now (something like 10x as fast) would greatly improve the game and level the field for warmongering civs.