A few years ago I would have agreed with you, but spending time in Germany has changed my view on coins.
See, in the US, coins are kind of useless on their own. You can't pay for anything with only coins, so giving exact change is always an extra step on top of paying with cash. Ugh.
But in the EU, they have €1 and €2 coins, and it's difficult to overstate how much this changes the dynamic. It means that for purchases under ~€10, it's suddenly possible to pay with coins only. It also means that for cash purchases, you can often receive your change as, well, change. So for large purchases, I'll pay with cash only and receive change, which goes in my coin pouch, and for small purchases I'll give exact change in coins only, using them up.
This actually becomes less onerous than paying exclusively with bills, like I do in the US, because you use up your coins naturally instead of collecting them in a jar or something to be counted later.
It also helps that taxes are included in the price label, so a €5.99 purchase will yield €0.01 instead of something in the vicinity of $0.75.