Ubulele, I enjoyed your post. I'm a relative novice to music theory and did have to take my time, going slowly through the explanation but I did understand it. It is a complex subject and sometimes a discussion can get beyond my ability to understand, given my limited background but I did get a better understanding of chord formation. Early on, I too was curious when I stumbled on two identical fingerings having different names and with my most rudimentary understanding of music theory, I wrote it off to the fact that with just 4 strings and limited reach one can only make a finite number of fingerings and in varying keys, some might turn out to be the same and that you will call them one name rather than the other, depending which key the music is written in. Kind of like why we use the sharp notation or the flat...it depending on the key. Your explanation filled in a lot of the blanks.
If one asks a question, one should be prepared for some pretty knowledgable answers here on UU. Sometimes I have asked questions as a novice where the answer or solution to a problem was beyond my scope (like a repair or adjustment) and I needed to defer to a professional, but sometimes with the explanation folks gave, I could do something myself, if I carefully digested what they were saying to me. This discussion seems to follow on those lines. The answer was given by folks with superior knowledge of music theory and one either makes the effort to learn more and try to understand it or just accepts it as an issue better left for the professionals.