I realized when reading your response that you use "tone" for "whole tone". So from my perspective you're overloading "tone", which could mean semitone, whole tone, or scale degree tone, to only mean two half-steps, but to me, it's like your perspective that in the article the word "step" is overloaded to mean one half-step. I think it is more useful, if you were to define fundamental unit of pitch as one half-step, since there are of course many intervals that you cannot describe with just a number of whole-tones. It's one syllable and corresponds to one note = 1, instead of the notion of "half" and then you have to explain how the difference between E and F is '1 half', I think it is a mess.

And - I personally analyze music in semitones, not scale degrees. I find it much more useful. Even though that's not considered "standard" there are some things even standard theory has to use chromatic language to describe, like the tritone (you could get into "#4 or b5" but that would require a lot more than just saying 6 semitones).