If you're shooting a bolt gun you don't have to wait for gas to cycle the action.
Yes there are advantages to shooting a semi-auto. However, the rate of fire is not an important consideration, when only a couple or 3 rounds are to be fired under field conditions, which means potentially having to recover from heavy recoil, coupled with a moving target that can be obscured by either vegetation or atmospheric conditions like fog or blowing snow. If you're convinced that rate of fire is the ultimate consideration, you should dump your gas gun in favor of a double rifle, as no semi auto can fire as fast as a double, as both barrels can be fired in unison.
Under typical big game hunting conditions, the semi auto rifle's biggest advantage is that you don't have to break or adjust your firing grip between shots, and that advantage is huge. Then again if you live in Texas and from a helicopter need to deal with a marauding herd of wild hogs, an AR with a stack of 30 round magazines is probably your best solution. An often overlooked advantage is that a semi-auto can't be short stroked in a high stress dangerous game scenario, which is another huge advantage. Most gas operated rifles reduce the felt recoil of firing powerful cartridges, Pounder once had a BAR converted to .458, and it didn't feel much like a .458 or for that matter a .45/70. Ultimately it was an interesting experiment, but didn't seem practical for his purposes, so he went back to his Brno 602. A recoil operated semi-auto though will pound you as hard as any manually operated rifle chambered for the same cartridge though.
The primary disadvantage of semi-auto rifles is an almost universally poor trigger, and attempting to improve it usually messes with the piece's reliability. I've sold a few bolt guns that I was unable to tweak the trigger on or was unable to find an good after market trigger for, and because I'm admittedly anal about the importance of a good trigger, I'm not much of a gas gun guy. Having said that, I do own a few at the moment, including an expensive AR, which shoots sub MOA but doing so is a challenge with that trigger. A secondary disadvantage of the semi-auto is the fewer chambering options that are available in factory rifles compared to bolt guns. A BAR in .375 Ruger might be interesting for example, but you won't find one any time soon. Since the BAR is available in .338 Winchester, the problem isn't dramatic though. Personally I don't consider reliability a weak point in a quality semi-auto rifle. Machinery does repetitive tasks with far greater precision and reliability than people can, in all sorts of applications, and cycling the action of a firearm is a pretty simple task. All it asks is that the firearm be in good mechanical conditions and the ammunition be dimensionally uniform and produce enough energy on firing to fully cycle the action.
The bottom line is that semi-autos can be an excellent sporting rifles for the fellows who appreciate them, but they aren't for everyone.
