1. p.35 of Richman's Book suggests keeping the same fingering for the 3 inversions of major and minor chords in all keys. Richmann admits that this is, at times, (physically) awkward but says that it saves on thought time and is an intelligent compromise.
I wonder if he thinks this will work for a Liszt-like chromatic run up the keyboard using all 1st inversion triads, legato.
No, I believe Richman is suggesting to follow the fingering only when sight-reading, not when performing difficult solo works (after all, the book is about sight reading).
The musical shapes, phrases, or notes that lie before or after the particular musical shape in question usually dictate the fingering that'll be appropriate.
Wouldn't a better goal be to memorize all the chords with the most physically convenient fingering?
Fink does say that developing a "hand vocabulary" will lead you to use identical fingerings for identical musical shapes, but of course this isn't always physically possible (comfortably).
But I believe he emphasizes "identical fingerings" to urge the pianist to become comfortable playing in the "black area," which consists of black keys and the parts of the white keys nearest to the fallboard, with any finger, and anywhere along the length of the keyboard. Since the black area is the furthest away from you, arm movements are required (but they always are). I believe this is one of his aims: to accustom the pianist to back/forth movements of the arm in musical context.
There are a few chords where it might be more comfortable to susbsitute a finger, but if you ingrain the "inversion pattern" into your brain you will be able to hit a major/minor chord in any inversion at the drop of a hat without a moments hesitation and that is what Richman is aiming for. Another benefit of using the fingering he suggests is that your hands will eventually hit the right notes almost by themselves and you won't have to look at them or think about it.