Maybe the annexed territory is more easily governed from the annexing power, but if politicians maximize all the time, this difference should not be too great at the time of annexation. Suppose, for instance, that the politicians of the annexing power can extract X from the annexed territory, while present rulers there can extract Y. If X is less than Y, present rulers could compensate the potential annexing power to retain status quo and thereby avoid annexation, but as soon as X gets bigger than Y, this strategy no longer pays and so annexation occurs. The point at which annexation becomes optimal from the point of view of the politicians of the annexing power is when X is just bigger than Y, so total extraction from the annexed territory should not be very different as a result of annexation.
Maybe there is a fear among members of some minority in the annexed territory of persecution under the new regime, because their new fellow nationals are apt to hate them. If so, total extraction from the population remains about the same, but different segments of the population are affected in different ways. However, mistreatment of minorities could have been part of the compensation mentioned above for as long as annexation was not chosen. This would have been a likely outcome if the annexing power really was full of haters of this minority. Again, it is hard to see why, purely as a result of annexation, any ordinary citizens should worry much about changing legislation.
Yet, if we return to the situation in the Crimea, the Tatar population there must be quite up-to-speed about the recent developments, and I would not feel comfortable announcing their recent exodus uncalled for. So, what is wrong with my analysis of annexations?