@WittGenStein: It occurs to me that the specific content of your sentence may have limited the range of wording that seemed plausible to respondents.
Suppose Jack is the production assistant for a weekly variety show that is aired on the radio. Jack's boss has just told him he thinks they should ditch the band that has been playing regularly on the show for the past year.
Jack thinks the band's fiddle player is world class, but agrees that the other members are only mediocre. He responds:
"I agree, but not all of them. Jill, their fiddle player, is pretty damn good."
Now, though, imagine that Jack wants to keep Jill on for reasons other than her musicianship - unbeknownst to the boss (who is also Jack's brother-in-law), Jack and Jill have been knockin' boots after the show for months. So our protagonist dissembles:
"I agree, but these are tough times for musicians, we wouldn't have to ditch every single one of them, would we? We could keep on one or two... like, say, that fiddle player, what's her name again?"
Here, by using "every single one" Jack is saying that the ditching wouldn't have to be completely comprehensive, they wouldn't have to make a completely clean sweep, as it were. He could have said "all of them" in this sentence too, but would have been unlikely to stress "every single one of them" in the first situation.
(In my ears, "each and every one of them" would be equivalent to "every single one of them" here, but I am not sure whether Lonelobo would agree. Definitely though, "each" alone would not work.)