The U.S. has an extreme obsession with credit (and debit) cards, but cash is still much more common in many other countries.
Some of this is probably just due to historical accident, but some of it is also due to differences in the tradeoffs between the various payment methods in different countries.
In Japan, for instance, (1) cash is both easier to deal with in many cases (e.g. ATMs will happily give you very large quantities of it, a lesser crime rate makes using it safer, vending machine bill readers are much more accurate, shops are much more willing to deal with large bills, etc), (2) the presence of other mechanisms like very easy/cheap bank transfers replace some of the use-cases of credit cards in the U.S., and (3) credit cards are more restrictive (e.g. by default you have to pay your entire balance every month).
Also I think credit cards started their climb in the U.S. by replacing checks (which were in many ways very inconvenient), and that gave them enough familiarity and infrastructure to continue from there; in Japan, on the other hand, checks were never really used at all, so credit cards never had that "in."
As a New Zealander, I found the US to be obsessed with cash when I visited for tips, payments, transport etc. In NZ I was recently given a $20 note by a colleague who owed me some money, and I spent it. I commented to a cashier how small our 50c coin is - they looked at me funny and told me it had been like that for 5 or so years. I don't use cash. Never do. I don't have a wallet that holds anything more than 2 cards. I try to avoid cash and never have it on me. I can't remember finding this inconvenient in NZ as we don't tip and everything takes cards.
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.
Some of this is probably just due to historical accident, but some of it is also due to differences in the tradeoffs between the various payment methods in different countries.
In Japan, for instance, (1) cash is both easier to deal with in many cases (e.g. ATMs will happily give you very large quantities of it, a lesser crime rate makes using it safer, vending machine bill readers are much more accurate, shops are much more willing to deal with large bills, etc), (2) the presence of other mechanisms like very easy/cheap bank transfers replace some of the use-cases of credit cards in the U.S., and (3) credit cards are more restrictive (e.g. by default you have to pay your entire balance every month).
Also I think credit cards started their climb in the U.S. by replacing checks (which were in many ways very inconvenient), and that gave them enough familiarity and infrastructure to continue from there; in Japan, on the other hand, checks were never really used at all, so credit cards never had that "in."