I had a similar experience as an Australian tourist in the USA. Suddenly I needed a bunch of 1s, 5s and 10s just to handle tipping. It was very annoying.
So, in actual fact, there's two layers of annoying wastefulness at work.
Basically I used the small notes when my total was close to a round figure. I could leave a $1.39 tip on a $20 meal or I could add a few $1 notes.
Most of the time I used my card (which is another story) so I could do this more easily, but sometimes you're in a hurry and the extra steps involved in US dining are a pain in the posterior. Hence: carrying small bills to allow tipping flexibility.
