Is that book for jazzers?
No classical book would recommend 5-4-2-1 for D, E or A major in root position.
God forbid, but if your left middle finger is suddenly paralyzed, what kind of fingering will you play chord Db F Ab Db? There is a dry theory that needs to be learned; but there is also a reality that can impose non-standard solutions.
The reality is that you are far, far more likely to develop a contracture deformity of fingers (3,) 4 & 5 (Dupuytren's) - especially if you are male and of Nordic ancestry - or suffer a traumatic amputation of several fingers, or develop weakness of the three lateral fingers (median N compression) than a sudden paralysis of the middle finger with nothing else affected. It's the reality of anatomical and medical science.
Playing all arpeggios using the same fingerings regardless of the position of black keys won't help any of that in the least.
It is true that the piano beginner must learn the economy of playing movements and the rational fingering that matches the anatomical structure of the hands.
The OP is a near-beginner.
On the other hand, real piano life at an advanced level inevitably also includes uncomfortable situations requiring both rationalization and adaptation. Rationalization has been mentioned; the point of adaptation is to turn the inconvenient into the convenient. This requires separate work, provided that flexibility and freedom of the hands are preserved as much as possible. Students should also have an understanding of the realities of piano playing. The great F. Busoni recommended using in exercises the craziest fingering.
I play at advanced (classical) level, and use the fingerings learnt from my student days (scales & arpeggios etc) automatically, all the time, without having to think about it, precisely because they have been well-practiced & ingrained. (And they can easily be adapted to suit the music being played.) That's what all classical students need to do, to facilitate their learning of more and more advanced pieces.
When I sight-read (which I do frequently), this experience facilitates playing at the right tempo with all the phrasing, dynamics and nuances in place.
When I encounter classical music that requires awkward fingerings, I take them as they come and adapt accordingly......with minimum fuss.
Jazzers & poppers may have other priorities, like transposing songs into every key on the fly(?), so I presume that the OP has been told by his teacher to learn the K.O. way (whatever K.O. is). In real life, I don't perform jazz or pop, so I leave that to the experts in those genres, like you.
I rarely ever have to transpose pieces on the fly when playing (for myself or for an audience): the only times when I had to do so were when accompanying hymns and songs, for which chords are mainly required......like church organists. And classical pianists have to be able to play chords - including big awkward stretchy ones - in all permutations. It's usually anatomical factors that cause experienced classical pianists problems with them: for instance, I, with my small hands, can play some chords that my last teacher (a concert pianist with big hands) can't.