I think the primary realistic effect of a high percentage of citizens actually carrying (as opposed to just licensed) would be when criminals change their behavior out of concern that their crimes will be confronted by an armed adversary. Here in IL, where we have had concealed carry for just over one year, and where open carry is not legal, we have about 1% of the population that is licensed to carry concealed. Clearly we do not have enough carrying to make any dramatic change in criminal behavior, although I have not been reading about as many street robberies in downtown Chicago as I had been in the past (but now that the weather is warming up that might change).
I do think that when the perception is that many are armed, it tends to make people more polite and reduce the likelihood of emotional and irrational confrontations that might turn violent. Last summer while on a trip to Yellowstone National Park and environs, we stopped at a Starbucks for coffee. Waiting in line near me was an older gentleman with a huge handlebar mustache, and what appeared to be an M4 draped over his neck, as well as a large revolver holstered on his hip. At first I thought he might be an LEO but there was no visible badge or other indication that he was in law enforcement (such as handcuffs on his belt, etc.). What was most amusing was that no one reacted to this individual in any way. He ordered his coffee or whatever and then went on his way. I could only imagine the bedlam that would ensue if such an attired individual did this in a state like NJ or California or Maryland. The SWAT team would probably arrive within seconds, and citizens would be screaming and fleeing as fast as they could. But where this occurred (I can't now recall if it was in WY or in SD) it was accepted as normal, and my guess is that no thug would have dared try to commit a crime in the presence of this armed individual (plus however many, including myself, were carrying concealed).