And the answer is...
To answer the OP original question, and the following speculations, YES, there was a specific purpose, and NO, the full length so-called "Mannlicher" stock was not designed to reduce barrel harmonics, protect the barrel from shock, protect the hand from heat, emulate military carbines, etc.
The answer is in the name itself: "Stutzen" the German word for a full length stock translates in English as "Support". The 1903 6.5×54mm Mannlicher–Schönauer rifle was designed with a full length stock at the request of Archduke Franz Ferdinand Carl Ludwig Joseph Maria of Austria (the one whose assassination on 28 June 1914 in Sarajevo triggered World War One), nephew of Emperor Franz Joseph I of Austria and heir presumptive to the Austro-Hungarian throne after the death of Crown Prince Rudolf in 1889, so that he could actually use the short barreled and full length stocked rifle as a handy climbing help when hunting Chamois (French) / Gams (German) in the Austrian Alps. His Imperial Highness apparently liked to put the short rifle stock butt on the big rocks he had to step on or step over, and use the conveniently short rifle and appropriately thick muzzle in that manner, as a walking stick to help secure his balance and/or help a big step up. All those who have hunted rough rocky steep slopes will instantly understand the concept...
If memory serves, I learned this entirely by chance eons ago, reading a non-hunting related book, the 1964 The Arms of Krupp by William Manchester. If memory further serves (?), and without pulling my 1903 out of the safe, I believe its barrel bears the inscription Krupp Stahl (Krupp steel)...
