The rise of "all of the"

Solution 1:

The popularity of certain words, phrases and idioms may see dramatic changes at certain points of history.

makes sense:
(1800-1950 AmE)

Wonder what triggered the spike post-1930. Some quote has caught on well and everyone scrambled to use the phrase? Makes sense to me.

Solution 2:

The question used English, corpus = 0 as the data set for the analysis.

I ran ngrams queries for your phrase "all of the" for each of the other corpora: American English, British English, English fiction and English One Million. All showed a similar, and quite smoothly increasing trend of rising frequency between approximately 1870 and 1920, with one exception: British English, corpus = 6

Link to ngram

This might be worth pursuing. Without having the benefit of additional context, i.e. the motivation for your inquiry, I can't provide any more specific insights.