Replacing dollar bills with dollar coins doesn't change transaction prices, just the tokens used for the transaction. Junking the penny does change prices.
I'm not convinced of this. MIlitary stationed overseas frequently find themselves penny-less... base exchanges, stores, restaurants, etc. just don't find pennies worth carrying. Instead, prices are rounded up or down to the nearest $0.05. I spent a lot of time overseas, and I never heard anyone complain that they missed pennies. Personally, I'm ready to eliminate pennies, nickels, and dimes... going straight to the quarter. A nickel doesn't even buy more than a couple minutes at a parking meter these days.
Currently, nearly every jurisdiction has a sales tax. Tax calculations inevitably produce transactions at the sub-penny level: 7.25% sales tax means a $1 purchase requires 7 + 1/4 pennies. We obviously don't have sub-penny units, so we just round down to 7 pennies. Other transactions round up, I'm sure. In the end, someone could game the system by using advanced models to ensure more purchase combinations result in rounding up, but really... at a penny per transaction? I doubt many businesses would risk the bad publicity... and even if they did, it's probably a lot cheaper for consumers than paying for all that change to be lugged around, counted, and transacted.
In short: This week, I spent several minutes in a grocery store checkout... behind an old woman counting change and looking in her purse for more.