I am in no way qualified to answer the linguistic part of the question, but I can contribute something about King Ludwig.

As king of Bavaria, one of the largest and most important regions of the Kaiserreich, Ludwig was a remarkably ‚dreamy‘ person for his position. He is most known for building castles, and his enjoyment of the arts. Richard Wagner was a prominent recipient of support.

Ludwig had always had social fears, which heightened as he became more isolated during his last years. The contemporary diagnosis of schizophrenia, mental weakness, and paranoia has been debunked, however. He never - even in complete isolation on mountain sides, and in small cottages - neglected his governmental duties, which was not factored into the decision to try and incapacitate him.

What drove me to write this answer is the ‚Mad‘ that was added to his name. In German-speaking countries, King Ludwig II. is widely known as the Märchenkönig, the Fairy Tale King, for his inclination to support the arts and build romanticizing castles (and living in his own world at times).

While I cannot speak to the other examples, these added names are often to be taken with a grain of salt. It may be political adversaries who coined the name, or later historians who wrongfully added it.

A good example I can attest to is Arnulf der Böse, Arnulf the Evil. His name stems from monasteries, where monks wrote down the history of the early 10th century, only to be appalled by his secularization of church/monastery lands. They looked at it through their lens from a few hundred years later, and determined him to be evil for inflicting losses to church possession. That it was common practice in the early 10th century, so much so that every ruler did it in some capacity, got lost in history for a minute but their nickname for him stuck far into the 20th Century.

Unless someone is called the Fat, the Clubfoot, or the Hook-nosed, in other words obvious physical features, one of my professors always cautioned against reading into these names too easily.