Unfortunately(?), their power made them so paranoid they refused to marry outside of their family, leading to disgusting inbreeding, and their downfall. In some ways, they are a microcosm of many facets of the German phenomenon.
I can say this as someone who is 1/8th German, namely from Brandenburg, Hesse and Rheinland-Pfalz, it is something I have very mixed feelings about.
So to clear a few things up...
The "Germans" was not the name they used for themselves, and more or less, still is not today. That name Germani was given to them by the Romans, and fell out of use with the collapse of the Italic Roman Empire. Use of the term “German” to describe German speakers was revived in the mid-16th century namely by English speakers, based on the Latin name for the people. Prior to this Germans were called Saxons, Dutch, Teutons etc or more specifically Schwabian, Bavarian, etc depending on where they came from, by the English. Calling them “German” increased in popularity with the rise of German nationalism and the nation-building that resulted in the closest "modern" equivalence of the country in 1871, which was spearheaded by Otto Von Bismarck.
As someone who grew up quite a bit in Wisconsin, a state known for their German heritage, I'll say this:
I have no idea what it means to be German. Most of the people calling themselves "Germans" came to the U.S. before Germany was even a country. The Roman term Germani, wasn't exclusively descriptive of any singular language. Barely any of Germany as it stands today was in actual Roman controlled territory, yet they named their most notable administrative function the "Holy Roman Empire" close to a thousand years after the fall of Rome, co-opting Latin supremacy when convenient, only to eliminate most of the Latin "loanwords" they'd co-opted, upon the German Romanticism movement led by linguists such as August Zeune. They spearheaded the most racist vile movements of the 19th century, culminating in the Nazi regime. Literally central to Europe, yet pretended they were somehow more racially and ethnically pure than any other demographic. Bismarck is a great politician, but problematic in a variety of ways. Lately their most recent contribution to American culture is Mr. Drumpf.
Drinking yourself to oblivion and trying to run your body off cheese farts is about all I can think of (that isn't expressly problematic to other cultures) when it comes to being "German", especially when it comes to German-Americans.
This is something I think that is characteristically "German", defining yourself in opposition to others. And that's what is wrong with "German-ness" fundamentally. It speaks to an enormous inferiority complex. And a blinding sense of irony.
Back to August Zeune, a linguist at the heart of the German Romanticism movement. He fought against the use of foreign words in the German language, yet is especially notable for popularizing the use of the term "Balkan Peninsula" for the landmass between the Adriatic Sea and the Black Sea ("Balkan" is a Turkish word, and geographically, under no scientific sense of the term is the region a "peninsula").
This is a common phenomenon you will find analyzing any country in the 19th and 20th centuries especially, when the nationalistic movements were at their peak; purifying the language of foreign influence. Synthetic division. Being antagonistic and out of artifice, instead of letting the words you speak reflect the truth of genetic and/or cultural influence.
And it has brought numerous empires to collapse. And it will happen again.
Worth taking into account that the Abolition movement in the United States was started primarily by Mennonites and "Quakers" who were of mostly "German" descent. It is apparent that the boundaries between "good and evil" are not as distinct as some would like to claim, and so condemning entire ethnic groups is unjust, even while a prevailing spirit of supposed superiority based on genetics might be present in said ethnic group.
I would have a hard time believing that a linguist such as August Zeune would be ignorant of his own ideals when it comes to his own language, and did not purposely equate the region with a term that in English "balk" literally means "to be unwilling to do something or to allow something to happen, to stop abruptly and refuse to move". It would seem intentionally disparaging to me that Mr. Zeune popularized a term that sounds to a Western or English ear like the word Balking, or informally, Balkin', as if to say, the region embodies that action. In German, "Balken" means bar, as in someplace that could be barred off. Sounds an awful lot like he's basically saying, "a place we don't go". It appears the Turkish word "balkan" meaning "mountain", has some relation to the English word "balk", comparable in meaning to "a reaction to something viewed as difficult or impossible", as a traveler would certainly "balk" at having to cross a mountain, in this case both stemming from Proto-Indo-European "bhelg". In any case, a more accurate description would be something like the Black-Adriatic Pseudo Peninsula, and is the term I would prefer to use going forward unless someone else comes up with something better.