The penny coin still exists for what reason?
Other than simple inertia and incompetence on the part of elected officials, which is also a valid reason, Conspiracy Theory suggests two possibilities, not mutually exclusive.
A. It is  psychological warfare against the general population. It discourages people from revolting. How? It reminds them of the futility of their piddling existences. Dicking with pennies every time they pay cash, they feel somehow useful, doing something with their hands, having a human relationship however brief, with a random cashier. Feeling a remote connection with a past when the penny was somehow useful for paying taxes at least, and when it actually functioned as a unit of purchase. Now it is still legal tender, but by law, a merchant is not required to take more than fifty of them in a transaction, as payment.

When I say it discourages the People from revolting, I don’t mean it is enough to discourage them from actually being revolting. This is largely a matter of individual choice.

B. The motto in God We Trust, reminds everyone that money, especially the Penny coin, is the Root of All Evil. Instead of the Penny, we should trust in God to deliver our Nation to Prosperity, since by one’s individual efforts, the chance of achieving that goal are almost nil. The Byzantine Tax Code practically assures, that only large corporations can afford the legal and accounting help to make a business prosper.

The First Amendment to the U.S. Constitution is supposed to prohibit Congress from making a law “respecting the Establishment of Religion”, but the Tax Code does the opposite, giving Churches and ministers of the Gospel huge tax breaks, while the dysfunctional, corrupt, and probably soon to be more oppressive Government bleeds most of the People dry.

Repealing the 16th Amendment which authorized the Income Tax, may be the only way to stop the madness.