In the US you pay in paper money and you're almost always going to get some change in coins. Pretty much that means you're always carrying around both bills and coins. The coins have so little value most people pay with bills and then just pocket the coins without counting them. At the end of the day the coins go into a jar, and eventually you have to lug that twenty pound jar to the bank or one of those coin machines.
Why not carry usable amounts of cash in coins instead? You pay in coins and you get coins back in change. Of course that doesn't work if need to carry larger denominations, but if you're going to buy lunch or pop down to the liquor store it's more convenient, IMO.
I'm the opposite. I carry a wallet-like thing anyway for cards and other misc paper. Paper currency is just a few more pieces of paper. Coins are another pouch or something that I need to carry. Although, to tell the truth, I pay cash so seldom in the US these days that it doesn't really matter.
My wallet includes a pouch for coins; I think that's fairly standard for a wallet sold in Europe.
Coins are easier to tell apart, and I never like the grubby $1 bills I get in the USA. But, I don't often use cash either -- mostly when splitting the bill in a restaurant, since it's easier to hand the waiter 200kr than have everyone use the card terminal in turn to pay their exact 194.23kr share.
One of the issues with coins for me is weight/volume. It wouldn't be too much work for me to have $20 in $1 bills in my wallet, but carrying around $20 in quarters (or even $1 coins, to be honest) seems like it would be much more effort, since it would take up a large amount of the space in my pocket and likely be fairly uncomfortable for my leg.
