Canada is phazing out the penny. No great surprise. Pennies are a losing proposition because they cost 1.6 cents to make while they are only worth 1 cent. The selling and distribution of all other currency makes money for the government. The difference between what it costs to produce and what the face value is worth (also could be called the "profit" of selling money) is called Seigniorage. The government lost 0.6 cents of Seigniorage (profit) for every penny produced. A nickel, assuming the same production cost, would be + 3.4 cents to the government coffers.
If the US government actually made the trillion dollar coin, then the Seigniorage would be $1T minus the cost of production of the coin. It's basically like subtracting one from infinity. The number is so large that the subtraction basically does not matter. We can round to a trillion (or infinity).
Despite the fancy word, every time the government makes money on Seigniorage it is essentially a tax. A tax that everyone seems to agree on because it is necessary for the foundation of our monetary system. More money that the government prints/distrubutes, the money profit they make. The government's incentive is therefore is to make currency that does not last very long in circulation.
Whereas the incentive for the user of the currency is for it last as long as possible that way the government collects less in tax revenue. Paper money can be destroyed, but it is pretty sturdy. A $5 bill can be kept inside your jean pockets while they go for a wash and tumble cycle, and make it out okay. But it eventually gets destroyed. Metallic money (coins) are practically indestructible. So, shouldn't users of currency want coins instead of paper money?
Not so fast. How much in coins are in your pocket right now? Okay, now how much in paper money is in your pocket right now?
If you can answer the first question while not being able to answer the second as well, I would be greatly surprised. Paper money is easy to keep track of. People lose coins all the time. Reach into the bottom of your couch, you will probably find some coins but no dollar bills.
Losing coins is a tax on those who use coins. This tax falls disproportionally on those who make a lot of small transactions using cash. This group is also known as "the poor" or whatever pseudonym that you find appropriate to call them.
By eliminating the penny in cash transactions, you have eliminated the Seigniorage on the poor. It is progressive policy. Now if we can only get rid of the nickel as well.
Fun fact: The last time the US eliminated a coin was the half-penny in 1857. Inflation adjusted, it would be worth about 7 cents today. Because it is now a collector's item, it is worth a whole lot more than that.