Reddit mentions of The Musician's Guide to Aural Skills: Sight-Singing, Rhythm-Reading, Improvisation, and Keyboard Skills (Second Edition) (Vol. 1)

I'm leaving out a lot of foundational material of course, and so far we're only talking about root position chords. But yes, this is a simplified yet expandable way of looking at four-part writing.

But you're always going to run into people who have problems with any system. Complaints I can see for the above approach:

1. "Not everybody plays a keyboard instrument." Keyboard-style harmonization is useful for conceptualizing voice-leading, regardless of context. And, you know, not everybody is four people who can sing SATB arrangements.
   
   
2. "This information isn't presented in the generalized form we get from SATB rules." Scientism rears its ugly head again. Most things in music are not reducible to a general formula, and a hell of a lot of it is based on conventions. (And, actually, voice leading can be generalized to an extent. Leah Frederick had developed some voice leading applications of geometric theory. See this presentation from last year's SMT meeting and this presentation from the year before. Derek Remeš also presented an interesting taxonomy of texture in figured bass realization in 2017.)
   
   
3. "You have to learn the rules twice with this method." Not really. There are differences between keyboard-style and SATB-style voice leading, but they feed back into each other.
   
   And there are other complaints that are usually lobbed at music theory curricula or music theory as a field generally, but I won't enumerate them here. What I'm presenting here is a form of figured bass pedagogy, which students are notoriously (and wrongly, if you ask this theorist) resistant to.
   
   Keyboard harmony classes are not as common as they once were, for various reasons. Joel Phillips (co-author of The Musician's Guide to Aural Skills) teaches theory and musicianship with a strong attachment to keyboard skills and technique, but I don't know of other curricula that are structured this way. I'm sure they're out there.