I guess it all depends on what you grew up using, but the guys who are used to pump shotguns would be making an easy transition to a pump-action rifle. I don't think I fired a pump gun of any kind until my early 20's when a buddy invited me to go duck hunting with him. I bought a Mossberg 500 and have used it to learn all sorts of new cuss words while missing everything from quail to goose. I have never gotten used to cycling the action automatically, despite shooting more than a few rounds of trap with it and it has always felt awkward, in my hands. I much prefer a semi-auto, O/U or single-shot.
Also, the bolt-action rifles I grew up using, both 22LR and the bigger center-fire stuff, were just so accurate, I couldn't imagine sacrificing that for a faster follow-up shot. In fact, I must confess to only taking one rapid 2nd shot in 25 years of hunting. I was 16 years-old that fall and was shaking like a leaf when a giant of a buck (that's how I remember it!) stepped out at less than 100 yards. I proceeded to miss that deer four times and if I'd had a pump or semi-auto, I would have missed him twice as many times!
I think the reason the majority of big-game hunters these days use a bolt-action is the same reason you see so many break-action single-shots being used by the TV hunters...the only shot that matters, 99% of the time, is the first one. I suppose it has to do with HOW a person hunts, and certainly still-hunting does lend itself to shorter guns with faster follow-up shots, but few people have enough land available to them to hunt that way. Also, it is more effective to hunt white-tailed deer, our most common quarry, from some kind of stand than by trying to sneak up on 'em. That makes for shooting opportunities where the first shot can be carefully placed, greatly reducing the need for a second shot.