I recall someone coming on afternoon TV - Merv Griffin or something - before 1970, advocating that we get rid of the penny. Everything could be rounded up or rounded down. People's objections were mostly irrational, believing that the pennies they had thrown into jugs, or obtained by children for returning soda bottles, or found on the street, would somehow no longer be honored, and society would collapse. For no reason that is not easily answered in fifteen seconds, we continue to have pennies.
Whoever Merv was interviewing then was right. Since that time, inflation has made dimes worth just about what pennies were then. So pennies, nickels, and dimes should be gone. No one uses dollar or half-dollar coins, generally, so we have already demonstrated we could do without them. Yes, the Brits have a coin worth a pound, and somehow they have adapted and we theoretically could as well, but somehow we haven't.
That leaves the quarter. We have logically eliminated the need to use the other coins. So, is it worth still having coinage if there is only one type of coin? Maybe. But with machines reading dollar bills and parking meters accepting your credit card, I'm going to go out on a limb and say we no longer need coins.
*Kiddie Lit reference. Every children's book by this author recommended.