A thousand rounds in a year isn't really "high volume" shooting -at least it isn't to some of us. My Ruger 10/22 digests that much ammo during an average week. That said, I suspect most 336's don't see anywhere near that round count in a single owner's lifetime.
I got my 336 when I was 11 going on 12, and I never saw it as much of a "range toy" until recently. Over the course of the 34 years that I've owned the rifle, its only had about 2,000 rounds down its tube. I've put half of them through the gun in just the last five range sessions, shooting 200 rounds each trip. Even at this pace, should I continue it, I am not overly concerned about wearing the thing out. Since I live about 15 minutes away from a nice public shooting range, and visit said range an average of 3 days each week, there is a pretty good chance that I will keep the volume up with my 336.
While it is certainly true that any mechanical device will wear out eventually, it also true that periodic repair and parts replacement can compensate for this to a large degree.
Also, the .30-30 (which my 336 is chambered to) isn't a high pressure, high velocity round, as we all know. I would think that if you keep the pressure around factory ammo levels, a 336 so chambered would last a good long while even with volume greater than 1,000 rounds a year. You simply don't have the throat erosion issues and locking surface pounding high bolt thrust potential that you'd have with more modern higher performance rounds. If you shot lead bullets, which the .30-30 handles well, I would think that their use would extend barrel life even further. I also think that more wear and tear occurs from improper cleaning techniques than actual shooting where most firearms are concerned.
So, for me, I'll just keep shooting my 336 as much as I want, which is currently quite a lot. When parts wear out, I'll simply replace them or have them replaced until the rifle is no longer serviceable, doubting I'll ever live to actually see that day come.
JP