The inclusion of 'single' is a stylistic choice for the sake of emphasis, although it may also add a connotation that something is 'singular' (exceptional), as demonstrated by relevant definitions of both 'single' and 'singular' by Merriam-Webster:
(These are only excerpts. Full definitions are linked above)
7: having no equal or like : singular
Simple Definition of SINGULAR
grammar : showing or indicating no more than one thing
: better or greater than what is usual or normal
: strange or odd
Edit per changes to the OP:
"the x greatest y" is quite common. You can tell singularity/plurality apart by looking at y, but also by looking at x. So my initial point, that "greatest" is already singular, is invalid. But I still don't understand the significance of forcing the subject to be singular with x, even though y will never be ambiguous about this.
To dispel confusion, when the noun that follows 'the greatest' is singular, the addition of 'single' will first and foremost emphasize the superlative quality that is being expressed. This can be done with any superlative adjective (e.g., view 'The Single Worst Thing a Salesperson Can Do'). In speech, there will often be a high intonation over the word 'single', again a matter of emphasis.
Both the high intonation and the seeming redundancy of information are methods of making your ideas more strongly felt, much as underlining or typing in boldface can be in writing.
If this is still not clear, consider:
'I never, ever want to do that again.'
In this sentence, 'ever' takes high intonation and repeats (avoiding a double negative) the same meaning as 'never'. Repetition emphasizes how strongly the speaker feels about what he or she is saying.
Not all uses of English superlatives are singular in number (e.g., The Greatest Minds and Ideas of All Time, by Will Durant), and there is some disagreement as to whether or not it is grammatically correct to incorporate 'single' into statements such as:
“What can you say about one of the single most amazing locations on
the entire planet?”
(tripadvisor, user review)
'I always thought that was one of the single most important things a
prosecutor could do is to seek justice for the families of victims.'
("brainyquote" of American TV personality Nancy Grace)
Be they correct or not, these uses of 'single' before plural nouns do not force those nouns to become singular. They appear to be used solely for reasons of emphasis (and perhaps the aforementioned connotation that what is emphasized is exemplar or exceptional).