Several guys I have hunted with are looking into the bigger, slower calibers of hunting guns. The reason? They are tired of destroying game meat with high velocity rounds when the animals are close. One friend got his deer a couple years ago at about 40yds. Used a 270 win and lost about 1/3 the meat. It was a quartering to shot, so the only shot available was in the left front shoulder, into the vitals. Ruined the shoulder, half the ribs on the left side and half on the right side on exit.
Read the levergun forums or similar and read what the guys with the 444, 45-70 even the 35 cals are saying. Most usually ALWAYS post "eat right up to the hole" cause the caliber is large enough to drop the animal cleanly but not so much meat destructive shock.
Will the 338 fit in this category? Not sure, but certainly much heavier bullets are available for it than the 308 and a 225gr or 250gr, 338 bullet will plow through a deer or elk without the meat destroying shock of a high velocity 165gr from a 308.
Might just have a limited following like the 358 Win, but the 35's are somewhat coming back (as in 350 Mag?). Who knows?