I don't know if we should get rid of the penny or not, but I suspect that private issuers would respond to the current situation differently than the U.S. Mint.

The U.S. Mint has implemented a law against melting down pennies and nickels which, at current metals prices, could be worth more as metal than as currency.

The new regulations authorize a fine of up to $10,000, or imprisonment of up to five years, or both, against violators.

See more here.