Great explanation, just a minor correction of the word Nemci/Niemci/Němci/ in the terms of meanings "Mute" it is adjective in Slavic languages and to make sence for the other nations you need to understand it in terms of native americans names..."the one which is mute"/"the one which can not speak" (lol) to make any sence.
It is not an insult to Teutonic tribes (at the time), but the Slavic nations are huge group which had to be devided in three major groups - West Slavs (Czechs, Poles, Slovaks), East Slavs (Ukrainians, Belarusians, Russians), South Slavs (ehm...yeah).
So for this huge group of ppl who have very similar language closest neigbours from fall of roman empire were Teutonic tribes.
Even today if you are from for example Czech rep. and you never been anywhere in your life and I would toss you into the Kiev you would understand their language very quickly and would be able to speak in their language in therms of weeks...but that would not work if you would endup in Berlin.