Among the countries that today maintain the same constitutional order as they have for centuries are democracies. Switzerland, the United States, the UK come to mind. All autocracies that existed 100 years ago have been overthrown—multiple times in many cases.

In what way is democracy to be considered destabilizing?

Looking at history and at the present moment, one could say that instability is an inherent feature of human society, but that democracy substantially reduces that instability.