TS, you’re still not understanding the implications of the term Nasi and why it is that it was not used practically since chasimas hatalmud. A nasi is a position of rulership that is similar to malchus (there’s a reason why it was held by einiklach of dovid hamelech), and it has definitive halachik ramifications that are not applicable nowadays. It would be like calling him an actual melech, embuing him with the halachos of a king, or (if he were a cohen) calling him a kohen gadol or meshuach milchama – there are titles that we don’t just use on gedolim/poskim/manhigim.
I’d say exactly the same thing if someone called rav chaim the nasi hador; this has nothing to do with my personal feelings about the lubavitcher rebbe.