I have had the priviledge of hunting in some great places in Wyoming, Utah and Nevada where the elk were not pressured. In Wyoming, we saw a legitimate 380 bull but could not get to him as we were new to the area. My brother shot a 340 bull on that trip. In Utah, I saw bulls with cows that would not respond to calls in the 320-360 range. I shot a nice bull on the last day of the hunt. I drew a great tag in Nevada last year and we saw at least 60 bulls in a week (during November). The unit I was on has legitimate 375+ bulls and that is what we were looking for unless I saw something else that I liked. We saw some big bulls that either passed on ones that we didn't like, were busted up or didn't have a shot at. I shot a bull that I liked on the last day of the hunt. All of the hunting in Nevada was on public land and on ranches in Wyoming and Utah. These hunts were all fun and enjoyable as I liked the people I was hunting with and would hunt with them again. Do I want to shot a big one? For sure. Hopefuly a draw one of the great Wyoming, Utah, Montana or Arizona tags soon and chase a big one. Have I passed up something and wish I would have shot it later? Not in the long run. I love elk hunting and my wife and scared that the mounts with overtake the house, so I have to be picky. I love elk meat, but my family is in the cattle business so I have many contacts in the western states and also enjoy beef, just lesser amounts than I used to.
If you want to kill a big one (which is all based on your expectations), you can't shoot a small one first. If your priority is meat, the likelihood of shooting a big one is going to drop as you are probably more concerned about the meat than the antler size. I have done other hunts where the access to elk hasn't there. I still enjoyed the hunts, but they didn't have the thrill of seeing the elk in shooting range and deciding whether to shoot or not.