The US has Puerto Rico and other territories that do not share borders or a similar culture. So technically we should be an empire. I imagine other Western countries would fit this mold as well, perhaps even moreso by having monarchs who while not head of state, should be befitting of the name.
Why are there no more emperors in name? Is this a political correctness issue?
In the case of the US and Puerto Rico, we don't fit the historical definition of an empire. Or more accurately, we don't have a leader akin to an Emperor in power or position. There are elective bodies with real power running Puerto Rico and they don't exist as a tool to direct the President's personal rule.