Don't get rid of the penny
It will just further delvaue our money if we do. People say, "just round everything off to the nearest .05, well fine. Do that. And real quick you will find that the nickel is the new penny, so everything will cost you .01 to .04 cents more.
Dollar coins have been tried several times before, and are not with us as standard items yet. Half dollars are, but are very seldom used. You can get them, you can get dollar coins, but not in everyday change. Anybody out there remember the $2 bill?
Money is an idea backed by confidence. Paper money especially. Coins have some value, when made of metal, more when made of precious metals, but beyond that.....
Coins can be made of whatever the govt wants. 35 years ago I visited Austria (back when a Glock was a clock), and the Austrian unit of currency was a Schilling. The exchange rate was 20 Schilling to 1 US dollar. Schillings were further divided into 100 Grosschen. And one would get 1 and 2 Grosschen coins in change. They were small stamped aluminium discs. I understand that at one time they had been made of wood.
If the Govt says it is worth X then it is worth X, until the govt makes an "adjustment". We sell our money around the world today, making it worth what ever the market will bring, and right now, the market sucks. The world doesn't have confidence in us, or our money right now, and that isn't likely to change much until we face up to some facts and make some hard decisions on how to deal with them. If we make the "right" choices, things will get better. If we don't......