This aside, removing the lowest denomination of currency is just a sign that the US has become an expensive nation
I'll show my source of fact first:
Historic gold prices
Gold Fix
Mental book mark that, we'll return to it.
The thing is, a coin is not a single use item. It will be in circulation for years, if not decades so it will be used many times for it's face value, meaning the cost of production does not need to be less than the face value.
I think you've missed the point of my initial observation - it's vital that the specie in circulation be worth less as a tangible item than it's intangible (face) value as long as the specie is a "Fiat money" . Else-wise people will mine your money, convert it to a commodity, then re-sell the commodity for the true tangible value. The government would actually be giving away wealth with each tangible specie. Put at a very basic level, if I can burn a 1 dollar bill and get the same BTU energy as a barrel of oil, then the value of a barrel of oil is $1 dollar. But I can't get the same BTU out of burning a dollar.
In 1910, a model T Ford cost USD $950.00, in any color you'd like as long as it was black. $950 would get you 52.19 troy ounces of gold in 1910.
Today, 52.19 Troy ounces of .9999 gold would be about USD $175,000. But today, you can get that vehicle in chartreuse paisley if you'd like. (I don't judge.)
The US hasn't gotten more expensive - arguably, with increases in production efficiency and automation, it's actually less expensive. What's happened over time is that the specie has been devalued, sometimes by inflation, sometimes by government policy. Again, I'm not arguing that point - only that it is very, very dangerous for a fiat currency like the Dollar to have a tangible value greater than it's face value. President Trump's observation on the penny (Excuse me, one cent piece!), if it is an accurate quote HINT: it is, shows he does not grasp this point. A graduate of Wharton School of Business, twice president of the United States of America, appears to not understand the basic underpinning of the world economy.