Earlier quoted context omitted.
The point isn’t to be “right” — whatever you define that as. The point is to be understood. Use blackboard bold when it’s what people are most familiar with and will engender the least confusion. You call this the “tabs vs spaces” debate, but I’ve literally never heard anyone advocate your position until you did, just now.
> I’ve literally never heard anyone advocate your position until you did, just now Many mathematicians concerned by typography use real boldface. For example: Terence Tao's blog, Donald Knuth, Paul Halmos (author of "how to write mathematics"), and the famous journal "Publications Mathématiques de l'IHÉS" which is the undisputed gold standard in mathematical typography. They use real boldface for the number sets N, Z…
It is? Do you have any supporting evidence for this claim?
I just had a look at a bunch of recent articles, and I would very much dispute it. I saw nothing extraordinary, and found the fonts they used rather ugly (though of course that is highly subjective). The use of bold face to highlight theorem/definition/etc. numbers is IMHO very questionable. The boldface letters you praise stick out like a sore thumb, feeling as if they were being emphasized and highlighted when they clearly are not meant to be.