If I say our country is subordinate country of America, reaction from the people who heard it would be split into pro and con. But if one country which is allowed for autonomy in terms of internal issues but their national security is dependent of foreign country would be called not so much subordinate as protectorate, Japan has to be called protectorate of America because we are dependent on America in terms of national security according to the treaty between two countries.
Current situation stemmed from the defeat of Japan in WW2 and enforcement of American more than 65 years ago, now it seems as if Japanese are hoping to sustain such subordinate status, especially at the time neighboring China has been emerging as a military threat which is fostering public opinion to strengthen the relation with America.