***** NOT A TEACHER *****
I have some ideas (not "answers") to share with you regarding your fascinating (to me!) question.
1. Some books feel that we should use "the" with superlative adverbs. Thus: "ran the fastest." (Sometimes we should NOT use "the," but that is another topic.)
2. Some books feel that the omission of "the" is informal.
3. Some books feel that the omission of "the" is fine and makes no difference.
(I shall keep my opinion to myself.)
4. "of all" might sound a little better if we extend it. Let's say: "of all his schoolmates."
I shall now (try to) parse "He ran (the) fastest of all (his schoolmates)."
He = subject.
ran = verb.
the = definite article that modifies (belongs to, attaches to, etc.) "fastest."
fastest = the superlative of the adverb "fast."
of all (his schoolmates) = prepositional phrase.
NOW HERE IS THE BIG PROBLEM: What does the prepositional phrase modify?
I googled many hours yesterday and discovered at least two theories:
Theory #1: It modifies the adverb "fastest."
Theory #2: It modifies the subject ("He").
Which theory is the correct one? I shall keep my opinion to myself.
P.S. I came across an argument in favor of theory #2. Is it correct? Of course, I do not know. A netizen named Jlovegren in the "English Language and Usage" section of the website Stack Exchange gave this analysis on December 23, 2012:
Bugs was [the fastest] [of all rabbits]
Jlovegren says that "of all rabbits" has a "partitive function." That is to say, "it introduces a reference set that the modified noun [my emphasis] should be compared against."
Jlovegren rearranges the parts of the sentence like this:
"Of all rabbits, Bugs [my emphasis] was the fastest."
I am not saying that this analysis is correct or incorrect, but "of all rabbits" does appear to modify "Bugs."
(Yes, Jlovegren's example is a superlative adjective, not an adverb. But MAYBE the explanation also applies to adverbs.)
Finally, V.P. Kannan in English Grammar (accessed through Google "books") gives this sentence: "He runs fastest of all the students." The author claims that "all of the students" modifies the subject rather than the adverb. The author rearranges the sentence: "Of all the students, he [my emphasis] runs the fastest."
Student or Learner