Must be an American thing, I guess. Is EFTPOS (ie debit card) less common in the US than in Australia? Seems odd to provide a credit card service by itself. People don't pay for coffee and things on credit, do they?
I always pick credit at the terminal because it's faster and more secure than entering my PIN at some random POS, although the merchant then has to pay a credit card fee on that transaction.
But to answer your question: yes, lots of people pay for coffee with actual credit cards. Some like the budgeting, some like the rewards/cashback that come with many credit cards, and some people are just bad with their money.
Don't forget that there is a lot of inertia in the States due to the huge population. It would be much more difficult to role out a national payment network here than in Australia. It's easier to piggy back on the system set up by the credit card companies than it is to get all the banks to work together.
There are a couple of other factors that make cards more appealing here too. Sales tax is added at the till. Where I live it's 8.75%. This means I can't know ahead of time what I owe and prepare the correct coins and notes. Additionally, I use Mint to track and categorize my spending. It sounds silly but it makes it so easy to track my budgets when I pay for everything by card.
Also, the large majority of banks offer Mastercard/Visa debit cards where even though you press 'Credit', its your money from your Savings account. You get the benefit of more consumer protection via Mastercard/Visa, as well as contactless payment and sometimes not having to sign or enter PIN