Or neck down a 9x57. The 338 is just about half way between the 8 and 9mm. The problem being it's an in between 'cat...half this and half that...with no real need. Too long for a short action and there are plenty of 338's cartridges for long actions with a lot more pizzazz.
The 9 and 9.3 mm's fill in the need. I would bet that someone somewhere has built on though.
I ran some numbers, 225 gr bullet, 3.20" COL necked down 9x57 and came up with 2500 fs at 52 KCUP rough figures...very workable in a re-barreled M98 8x57. Not quite up to the 338 Fed or a 338-06 which you could also re-barrel to in the same action, but not bad for those who like to play and have something different.
Basically a good idea whose time never came, then got left behind the bigger boys. I thought about it way back when I wanted to do something different with a Ruger 7x57 tang receiver. I almost did a 9x57 and if I would have I might have saved myself a lot of money later on messing about trying to get "the right one" done.
I built a 388-06 a few years later and have used it ever since. 35 years after the 338 I built a 9.3x62. Both work great.