I think if the US mint had their way, they would. Sadly Congress would need to pass a law to stop the cent coin and dollar note.
There are very strong groups which will lobby against the elimination of the cent coin or dollar note.
I also don't understand why the UK has not eliminated the 1 pence and 2 pence coins. I normally throw any 1 pence, 2 pence, and 5 pence coins that I don't need for my collection in a jar.
I am thinking that maybe in the future, I should keep any non-steel 1 pence, 2 pence, and 5 pence, and 10 pence UK coins.
Ken