It might be a little bit cumbersome, but I don't think it's impractical.
With only quarters and dimes it's difficult to pay $0.05 or $0.15, but it's possible. If I owe you $0.05, I must give you a quarter and you give me two dimes. Or I give you a $20, you give me $19 in paper money, three quarters and two dimes. If I owe you $0.15, I must give you a quarter and you give me one dime. If I owe you $0.95, I can't give you $1 and get change, I'd need to give you $1.25 and get three dimes back. Or give you $2, get three quarters and three dimes. Owing $19.95 or $19.85 would be most inconvenient, since many people seem to live life with only $20 bills in their wallet and there would be a lot of extra change required.
But, if we stopped minting pennies because they cost too much (3.7 cents), it's hard to imagine we're going to keep producing nickels when they cost 13.8 cents to mint. Dimes are much cheaper than nickels (5.8 cents), and quarters aren't too bad relative to face value (14.7 cents). Article with values [1], which I rounded to millidollars. I'd bet people would rather keep dimes than quarters, but rounding everything to quarters is a big step. I certainly would prefer quarters --- it's been a long time since arcade machines took dimes, and I only have quarter mechs (most of my games are on free play, and I can reuse the quarters I need forever, or add a credit button, but still).
[1] https://www.nbcphiladelphia.com/news/national-international/...