75% of the Swedes are pro monarchy.
The majority of the Danes are pro monarchy
The majority of the Norwegians are pro monarchy.
Of course the are reasons why we could get rid of the monarchy, but there just as many for keeping the royal families
The monarchies in the Scandinavian countries are democratic example for many other countries. So also the Netherlands and Belgium.
The royal families are above any kind of political bickering.
At least in Scandinavia they show a style and charm in behavior and language which often the politicians are missing.
Germany has a president who is not even elected by the prople and still has a symbolic and moral role which functions like a monarch, which seems to be the case with the presidents since the fall of the Nazis.
For many the historical traditions for having a monarchy is important.
For others it is that there is a continuation of a head of state in bad and good times.
Of course a royal family costs the country money. I don´t remember the numbers now, but a royal family costs less than your system with presidents and ex presidents over a longer period of time. As ex presidents and their family also need security.
On the other hand when you have a good royal head of state you have someone who has learned how to behave - not all politicians know that - often speak several languages, are good PR´s for your country, can express themselves in their own language better than some politicians.
For Americans who come from all over the world, having different backgrounds, but same language it is not same as living in a small country with a long history with the same background, same language, same religion, same history, same traditions.