Constitutional monarchy is a very broad term, covering everything from the present UK, where the monarch's power is purely theoretical or ceremonial, to Germany before 1918, where the monarch's power was almost unlimited. The Kaisar appointed the head of government, was the commander in chief, and could (and did) dissolve the parliament. The main limit on his power was his own incompetence.
Yes, some of the small states in the empire were democratic, but that only added to the instability of the whole after 1918 as the Weimar Republic struggled to unite people with very different histories.
Presidents have had similar powers in many presidential republics. For example, Finland was like that until ~30 years ago. Ultimately it doesn't matter much if the head of state is a king or a president. It doesn't even matter that much what they could do in exceptional situations, or whether they inherited their position or were elected to it.
What matters is the tradition of running a normal democracy. If the elections are fair, if the ones who lose their power step down gracefully, if there is a peaceful transition of power, and so on. If you have a tradition of that, adapting a different form of democratic government is not that hard.
Yes, some of the small states in the empire were democratic, but that only added to the instability of the whole after 1918 as the Weimar Republic struggled to unite people with very different histories.