Some coins are relatively expensive - the nickel, for example, costs more to produce than it is worth, but the dime doesn't and the quarter doesn't.

It's certainly possible that we see the eventual elimination of the nickel with inflation - even before getting rid of the penny, the US previously had a half penny for the first half of the 19th century that was eliminated shortly before the Civil War - but coins have benefits that paper money doesn't. Paper money is less expensive to print than coins, but it's not free (it costs about 4 cents to make a dollar) and it has to be replaced way more often than coins do. That's a big part of why the Euros have been so big on coins for so long (there is no one euro bill). Coins also appeal to collectors in a way that paper money doesn't. You can sell a quarter that costs you 10 cents to produce to someone for 25 cents.