Well, no. I mean, kind of, but you're looking at profit when you should be looking at value.

The cost to the mint doesn't really matter. The mint isn't a profit-making enterprise. If they were, they could just sell their hundred dollar bills for $200 and, like, where else are you going to get a hundred dollar bill?

Instead, the job of the mint is to circulate value. The value of each coin essentially starts over each time it's spent. Each you spend a penny, you've received that amount in some other form of value. So if a penny is spent twice, then two cents have circulated through the economy. This is essentially how the gdp goes up everywhere - the more time money changes hands, the more people receive value. So a penny that costs 2 cents to make has earned 4 cents in value if it's spent four times.

I'm a penny agnostic, so I don't really have a dog in this race. But the problem with the value of pennies is that they're not spent twice before they leave circulation - the overwhelming majority of them are left behind couch cushions and change jars, or thrown away, and never heard from again. If we were spending each penny twice, then we'd be earning back what we spent making the money in value to the economy, but we just aren't, and that seems like a big waste.