As a long term student of astrology, who expects never to be other than a student, I agree wholeheartedly that ignoring vargottama and neechabhanga is unimaginable. Just from the practical charts I have come across where the effects of these are fully experienced, I am convinced that these are valuable and unignorable aspects of a chart. I am quite puzzled at an experienced astrologer ignoring them - possibly there are times when they do not turn out as expected due to other configurations in a chart, but that is no reason to do so.
For my 2 cents worth - vargottama planets are stubborn in their effects, as is a vargottama ascendant. Neechabhanga can give sudden and unexpected changes in life. And retrograde planets have almost a karmic feel, a debts to be paid/collected type of effect. I may be completely wrong and would be willingly corrected.
I must say that I have not read this particular book by James Braha. I have read another one of his books, but generally prefer the classics or commentaries on the classics, as they tend to address complex issues more interestingly. Unfortunately, as I do not have a teacher, or the ability to effectively absorb and integrate everything I read, I remain an interested student.