I am agnostic on this question, but Jay L. Zagorsky presents the case for no:
First of all, the Mint creates coins in response to demand, and demand for small-denomination coins is soaring. Over the past decade, the Mint roughly doubled the number of pennies and nickels it shipped. Both coins enjoy widespread popular support in opinion polls as well.
It’s true that it costs more to mint these two coins than they are worth. In 2017, it cost the U.S. Mint 1.8 cents to make each penny and 6.6 cents for each nickel. Overall, however, the Mint is a profit machine. In 2017, it earned almost $400 million in profits producing circulating coins. For every dollar’s worth of coins it shipped out, the Mint made 45 cents. That is a profit margin many business owners dream about.
So, think of pennies and nickels as the Mint’s loss leader. They help create demand for more profitable coins in the cash economy. Eliminating pennies and nickels could make people think coins overall aren’t useful. And if we stop using all coins, the Mint will lose $400 million of profit a year.
…Stores and other businesses bothered by small-denomination coins can set prices so the final cost ends up in round numbers that eliminate using pennies or nickels. Food trucks and restaurants have used this kind of flat pricing to speed up checking out.
At the WSJ link, Henry Aaron argues the other side of the issue. I should note that I have acted privately to abolish pennies (and occasionally nickels) from my own life. Think of it as unilateral privatization, quite literally an idea for the trash and gutter.