Why do superlative adverbs sometimes use 'the'?

Collins Cobuild English Guides [3] ... Articles has the following to say:

Superlative adjectives tend to occur with the definite article, for example 'the tallest', 'the cleverest', 'the fastest'. This is because they refer to the item ... which is extreme ..., and ... therefore readily identifiable.

Superlatives are often used [with the obvious noun deleted]:

The old jokes are the best. [The old jokes are the best jokes].

Deletions follow different patterns, and quite often leave relicts whose part-of-speech is perhaps best classed as 'ex-adjective' etc (if one insists on assigning everything a POS):

She is the fastest runner.

She is the fastest.

She is fastest.

Sometimes, the definite article must be included:

She is the fastest I have seen.

...

A complication may be thought to arise when adverbs take the same form as adjectives:

She ran [the] fastest [of all the competitors].

She ran the fastest {cf faster than} I've ever seen her run.

However, this is a standard usage of the definite article, as seen with an ly-form adverb:

She ran the most smoothly [of all the competitors].

contrast the adverb-modifier usage:

She ran most [= extremely] smoothly.