This is sort of like OCD, it can ruin many peoples lives. What is described here is quite ridiculous, why is playing octaves so important that it requires so much time dedicated to it every day of your life? Mastering the circle of 4th/5ths chords, scales and progression over varying rhythmic accompaniment seems far more interesting exercises if you really must do hours of exercises a day! In terms of improvisation of stride/rag piano simply playing scales or scales in octaves all day is not going to help you a huge amount (in fact it is not going to help you anywhere an incredible amount, scales and octaves are only a small piece of the tools used in music!!).
A big danger when learning an instrument is getting overly obsessed with something, it distracts you from progress. I've had students obsess over a single piece and refuse to move on until it is an image of perfection, what a waste of time. So too I see practicing octaves in the fashion described here to be obsessive and a distraction to progress. Heck you might see some progress but it will be accompanied with a huge amount of inefficiency and long plateus of meagre improvement. Putting your tim and efforts into more effective studies is logical.
I just randomly had a read of a passage on the link in the OP:
"When playings arpeggios, the thumb is never used on a sharp key (black key) with the sole exception of the Gb major and Eb minor arpeggios, where the absence of naturals (white keys) in the triad necessitates the use of the thumb on a sharp key. Indeed, arpeggios consisting entirely of black notes (Gb major, Eb minor, and Gb major sixth), are fingered exactly as if they consisted entirely of white keys."
This kind of generalization is misleading and misinformed and a product of playing scales mindlessly and robotically. The fingering in scales can be various, the problem with simply playing scaled over and over again with the same fingering is that you will not realize how you can alter it in actual pieces. A single scale can be played so many different ways. Actually playing scales with octaves only takes away the knowledge of fingering also, so octaves scales although they may help you understand shape of the scale on the keyboard they do not help you understand your fingering options at all.