I'm not sure if you've heard Horowitz's live 6th rhapsody, but I sure as hell cannot crack a whip at the speed he plays the last burst of repeated octaves. Can you?
Have I heard it?

When I was 14 or 15, I was
obsessed with the Horowitz recording of this piece.
I practiced it relentlessly until I could match his speed (lol) even timing myself with a stop watch.
(this means I've known the piece for about 48 years!)
So, yes, when I really practice I can play it that fast -- and that's not the hard part -- the speed --its the endurance, shifting and cycling the work load, and pacing, IMHO.
But I learned to play octaves pretty well, and the trick is that its from the shoulder, with fingers on the key and I play with all my piano playing equipment, relieving and rotating to different muscles as needed while others refresh. It is sort of a "perpetual whip-like" motion with the wrist rising at times, going lower, changing fingers from 4 to 5, and whatever you need to accomodate the passage being played, while you cycle with
rounded movements to different muscle configurations.
Actually, I think Byron Janis has faster octaves, and maybe Martha Argerich (though I don't find her playing interesting a lot of the time-- just fast.
But the fastest and most easily played octaves I ever saw were played by Rudolf Buchbinder.
I saw him do this when he was 19 -- it was a good bit faster as was the entire Beethoven Concerto #1. I found it unbelievable at the time.
Go to 9:45 and shortly after you'll see him play the C Maj scale from top to bottom with one hand in octaves.
He also, as I recall, plays (or played) the end of the Waldstein third mvmt coda octave glissando, as octaves... not a glissando... crystal clear like a two handed scale. As I recall, his wrist was low, and his hand and fingers vibrated into the keys leaving only enough to go down the scale -- or up as in the case of the left hand, all initiated by the upper arm.
He was an incredibly gifted youngster who was accepted by the Vienna Music Academy when he was only 5! Which means he had to have been playing since he was at least 4! There is simply nothing he cannot do at the piano, though he probably couldn't explain it since he learned basic technique probably before he was 7! He's quite Viennese with a kind of happy go lucky personality, an immense repetoire, huge number of recordings, and doesn't spend more than 3 hours a day at the piano and never has.
But back to the subject, I think the way to learn quick, fluent and comfortable octaves, is to play them in groups... 4 quickly in a row, then another four, finding the best fluid motion, then finding how to "cycle" between the two groups then add another group, etc.
Oh, and the hardest part of the HR6 for me is the last part when I'm tired and have to play the chromatic scale in octaves in opposite directions. I think the trick for this, is to learn the chromatic upper and lower notes using the 4th and 5th fingers, and if you can use the 3rd finger also, attempting to mimic a similar idea as in Chopin Opus 10 No 2.