I agree the reduced sound could help some. The argument on them improving accuracy has to do with changing barrel harmonics (random and could be a positive or negative affect). But more so, removing the turbulent gas that flows out of an unsuppressed barrel right at the muzzle where the bullet is most susceptible to it.
OP's question has probably been answered, but for future people reading, hopefully this thread sheds light on the conversation. I've put a lot of thought into this as people personally ask me at the range or when talking hunting. I am not a guy who likes to speculate or to tell people what they should like or dislike, or how they should do what they want to do. I like to stick to the facts and let the arguments stand for themselves, so people can weigh them out.
With suppressors, it is repeated so often that people wish they would have bought one sooner, I have tried to understand why that happens and try to reframe the discussion into a way that can convey why people love their suppressors and talk about how it completely changes things.
All the talk and speculation about a suppressor's effect on the rifle is just that, a lot of speculation. In the end, I think the greatest effect it has is on the shooter. A bad shooter makes good guns bad. I have seen it time and time again. I used to shoot 1" groups and my buddy shot .25 groups with my same rifle. I trained and improved. I fit my gun to me and improved. I obtained better gear and improved. I bought a suppressor and improved. The suppressor also makes hunting more pleasurable, except the extra weight and length. But, the weight and length are solved all the time with shorter barrel rifles and ditching a needless piece of gear. In the end, muzzle velocity doesn't matter as much as precision. Bullets that pass through both lungs of any animal will kill it at the appropriate velocity for expansion. I know guys that kill out to the same distances as I do with "lesser" non magnum cartridges.
It comes down to the opinions you hold and are you willing to reconsider them. A person who doesn't want to change their rifle for any reason, won't buy a suppressor if it makes it too long. That's a perfectly rational decision. There is no right or wrong on personal preference or the weight you give different factors. The thing with suppressors is that it is so lopsided, the vast majority of people hunting with a suppressor will never go back.
NOTHING else I have seen has the same effect on a shooter as a suppressor. Most who adopt a suppressor will give up almost everything else about their hunting rifles, but won't give up the suppressor. It becomes the primary condition around which they build their rifles. Nothing is as dramatic in my opinion.
When it comes to "suppressors improve accuracy because of XYZ" I have heard all that and more. The truth is that at best there are hypothesis and guesses. Science hasn't really "proven" the hows and whys yet for some things people believe they observe. Some people make the argument on increased accuracy due to harmonics, etc. And, there is evidence that a suppressor will improve groups. But, the same mechanisms can also be used to argue why a suppressor would make it less accurate for the same reasons of harmonics by putting a heavy weight on the end of the barrel. And much of the same logic applies the other way around. The same gasses are there when the bullet leaves the rifling whether in a suppressor or in a brake or a bare muzzle. I could argue that trapping the gasses in the suppressor causes more turbulence around the bullet than into the open air.
I have talked about this issue and bandied it about with guys that shoot for a living, and they don't see a lot of difference either way. In some occasions, it helps, in others it hurts. It is usually marginal and they can't tell the difference over an extended period of time. It is just like putting a brake on a rifle. It can improve or make worse groups for any number of reasons. As a note, there are now tunable brakes and I have a couple friends who believe they can see a difference in the way the rifle shoots during and after the tuning process.
In the end, it doesn't much matter why suppressors seem to improve groups more than hurt them. But, to me, the most reasonable explanation is that a suppressor makes the greatest change to the weakest link in the shooting system--the shooter. If you think you have trained out flinch, then you are denying biology and the fact that your lizard brain reacts before your human thinking brain can do anything. Reflexes happen at subconscious levels of the brain that neurology is just discovering. Even with a suppressor, the lizard brain is still reacting to the recoil of the rifle moving. You can't do anything about it. You can make it a lot worse and you can make it a little better, but that is about it. A suppressor reduces the negative input into the lizard senses so the shooter isn't affected by it as much.
Now, I know guys, some record holding shooters, who can shoot good braked or suppressed. The thing of those guys isn't that they don't flinch, it is that they are so well tuned to the shooting process that they break the shot in a repeatable way so that they eliminate any possible error due to something conscious that they control. I've had the conversation with a couple, and we've talked about reducing the flinch, but they acknowledge that they can't control a reflex.
So, for the majority of hunters who aren't out there shooting thousands of rounds every year, when you consider whether to get a suppressor or not, just realize that most of the discussion that centers around the pros and cons listed above, don't really capture the "feeling" that shooting suppressed gives you. It changes shooting and hunting in so many ways that you just can't comprehend, because you have never truly experienced the way it completely changes the paradigm for the people that buy their first one.
Consider that in this thread, I think of everyone who has said that they own a suppressor, only
@wind gypsy says he may or may not hunt with it. I am sure some people buy a suppressor and hate it, but I can't really remember anyone in any thread of people who say that.