Actually based on advertising around Washington, DC and the lobby groups that run those ads, there is plenty of money in the metal and paper industries to lobby both for and against coinage changes, because I have seen it the last time this issue came up. DC is so packed with lobbying firms that work on portfolios of every issue under the sun that you have to have lived and worked inside the beltway for a while to believe it.

last year they made 8.4BN pennies, which would be about 21 million KG of Zinc, worth about ~$40 million?

That's a lot of money, but not "change public policy" levels of cash, either.

On the other side, handling pennies is expensive for businesses and banks, I bet it costs at least that much. There are special interests on both sides of this.

I'd imagine you also have to take into account all coin to cash machines that issue gift cards for change, and take decent percentages. They probably make several orders of magnitude more than the mineral companies.

If their profit margin is around 8% or so, which I assume would be reasonable for mining & industrial firms, that's a really small amount and not worth the lobbying cost