Do you have more background or sources on where this idea comes from?
It seems like this is more just one particular interpretation of a use of tax rather than it being the "one true purpose" of all taxes. I would be interested to see examples of places where this was explicitly the stated aim of a newly introduced tax. From my distant memories of discussing tax in history at school, generally it was to pay off national debt. I suppose one could argue that the debt existed in connection with the public/private manpower point above. And there are plenty of taxes introduced for other stated means.
It seems like this is more just one particular interpretation of a use of tax rather than it being the "one true purpose" of all taxes. I would be interested to see examples of places where this was explicitly the stated aim of a newly introduced tax. From my distant memories of discussing tax in history at school, generally it was to pay off national debt. I suppose one could argue that the debt existed in connection with the public/private manpower point above. And there are plenty of taxes introduced for other stated means.