The one-cent coin is a waste. Minting it costs more than its face value. Even the five-cent coin buys less than a penny did a half-century ago.
Paper one-dollar bills wear out had have to be replaced much more quickly than one-dollar coins. Our wallets wear out faster because we have to dig for paper for a value that is less than a cup of coffee.
The government has the expense of warehousing one-dollar coins because people, out of habit, don't circulate them. The habit of avoiding the dollar coin is perpuated by the fact that paper one-dollar bills are still in use.