I'm not sure if I can give you a definitive answer as to the origin and function of the paradiddle. I imagine it was to switch the hands and because of the natural accent on the first beat, it kept the lead hand from tiring.
Some trivia to help if you have insomnia:
I have modern copies of Benjamin Clark's
Drum Book from 1797 and Charles Stewart Ashworth's
A New , Useful and Complete System of Drum Beating from 1812. In both of them, the paradiddle has accents on the first two strokes,
RLrr,
LRll. In Bruce & Emmett's
The Drummers' and Fifers' Guide from 1861 and Gardiner Strube's
Drum & Fife Instructor from 1869 (I have a reprint of Strube's list from George Lawrence Stone in his
Military Drum Beats for School and Drum Corps 1931- republished 1958) the paradiddle is written as played in modern form; an accent on the first beat:
Rlrr,
Lrll.
However, in Phillip A. Sousa's
The Trumpet and Drum from 1889, the paradiddle is listed with two accents again:
RLrr,
LRll.
By the time N.A.R.D. came around in 1933 and up through the PAS in 1984 to today, the paradiddle in it's traditional form has just one accent on the first of four strokes:
Rlrr,
Lrll.
If you want to delve into this type of stuff further, check out Jim Clark's
Connecticut’s Fife and Drum Tradition from 2011:
http://www.upne.com/0819571410.html
Or James Blade's
Percussion Instruments and their History from 1971. Or if you really want to sleep, but need to find out the importance of drums in during the 18th Century, try Raoul Camus' book
Military Music of the American Revolution from 1975.
Boomka- I got to play in the Basel Tattoo in 2012. You must have had a blast last year; I wish I could have gone. One afternoon, before a show, we got to go to a drum work shop with Ivan Kym, a great Basel drummer. Before the workshop, there was a slideshow history tutorial which showed the oldest surviving Basel snare drum from 1571. So who played the first paradiddle and what was it for?
.
Again, I don't have a direct answer but I can send you on hundreds of leads!