Meaning of "a" in the idiom "to a man"

"A" really means "one" as in "one in number". The SOED (1995) gives the same definition ( "Express. a limit in extent, amount or degree. a indicating a limit or point attained in degree or amount: as far as; to the point of; down to.") and this example: "B Montgomery Three months to a day since the beginning of the Alamein battle.". Thus, "to a" means "precise to the exact number of units contained in the whole that is being considered", precise to one unit".

Addition due to comments

1/ By "number of units contained in the whole that is being considered" is meant simply the number of persons, days, animals, things, etc. that a particular situation will necessarily imply. For instance, in the sentence "Thus by using a pile of stones from which one stone was set aside for each sheep that went by, primitive man was able to count his sheep to a head, or at least that is what, we, modern thinkers, presume."; it is clear that the "whole" is whatever totality of sheep is considered in any particular case of counting.

2/ It means here again that the whole period of three months that is being talked about went by exactly, and it must be those very three months that followed the battle since any three consecutive months do not have necessarily a total of days that is the same as any other sequence of three months.

3/ It is understandable, as I see it, that Webster should have categorised this form as an idiom since its interpretation departs from the usual one associated to the indefinite article.

ex.

• He gave it to a man in the street. This use of the article is the usual one, "some man", not one in particular, and there is an action that involves materially one man.
• He counted to a man the marching soldiers in the street. There is no action that involves any particular man in this case, no individual, undefinite as specified by the utterance but real, that would be the recipient of the action. No man is the recipient of the action.

I do not agree with user Edwin Ashworth (see comments) that the frequency of use has anything to do with the determination of the nature of a term as being an idiom or not, and as well I do not find this use of "to a" so rare nor that it should be undesirable in today's English. To pick up on user Edwin Ashworth's remark concerning "to a nicety", I can say that thanks to this ngram, the use of it has been waning, although, lately, a reversal in the trend has been recorded.