To be honest as a European I always envy the US and their $1 bills. Its a hassle to always have to carry around all these €1 and €2 coins which one invariably receives by the end of the day.
I don't visit the USA often, but I've found $1 bills to be dirty and worn — it's much easier for vending machines to accept a coin.
If you don't like carrying excess coins, you need to hand some over when you pay. If the bill is €11.85, hand over €12 or €22 rather than €15 or €20.
Today for a 3,30€ bus fare I handed over 4,40€. Lightening my pocket of coins is simple enough, but for physical transaction efficiency it assumes that both customer and recipient can do simple math in their heads. Your local educational system may or may not provide appropriate guarantees of this.
They can be very dirty thats true, but i just dont like carrying large amounts of coins. They all end up in a huge box in my home at the end of the day. I’d rather have some €2 bills.
Anyway, Im paying much more by card now these days so this issue is going away slowly.
How can you hand over €12 or €22 if you're not holding excess coins?
Up to €4 (in 1s and 2s) is not excess.
Depends on your definition of excess I guess.
I used to (20+ years ago, now) buy a few rolls of dollar coins a week from my bank. Amusingly, they added them to their currency order just for me - the bank manager informally made me promise I'd keep asking for them - that's how low the demand was. I enjoyed them for parking, and vending machines, and buying coffee. Even at the time, however, I thought they'd made a mistake by not making them $2 coins, instead.