Rich, I've been involved in traditional archery most of my life and number a bunch of custom bowyers among my small circle of friends. I can assure you with some certainty that wood qualities required for unbacked wood bows and for gunstocks are quite different. Bows are wooden springs requiring flexibility and the ability to return to original state with speed and little or no permanent deformation. rifle stocks require stability, impact loading for recoil (column strength) as well as workability. then there are the economic factors.
One problem with linseed oil and other "long-oils" in gunstocks, though it is very traditional (at least since the Civil war or so), is that it dries chemically VERY slowly and will continue to slowly penetrate the wood for years requiring periodic refreshing on the surface. There was an old adage about this that I don't recall quite correctly, something on the order of "once an hour for a day, once a day for a week, once a week for a month, once a month for a year, once a year for a life" or something like that.
In addition as it slowly dries/oxidizes it will actually contribute to the chemical breakdown of the wood's cellular fiber structure----this may not be an issue with our typical rifles. But on old museum specimens of military arms, where it was a common cheap way to finish issue stocks, one can see deterioration in the back of the action and recoil absorbing areas. However it was a cheap and rapid way to get arms to the men who needed them and having a rifle last a hundred years was the least of their concerns.
One way to avoid this is to use a deep penetrating but fast setting sealer prior to the linseed application. If memory serves me correctly a heavily thinned shellac was frequently used in this way. the modified linseed oils, lin-speed and others were designed to "set-up" faster before the penetrated too deeply--probably more for production reasons than for preservation purposes.
