Default rates on credit cards run 10% of the outstanding balances per year.
The high interest is required to cover credit losses and servicing costs. At present epidemic levels of deadbeat behavior, nearly all the major card issuers are losing money even at these rates charged.
When people pay them back, they are a profitable business - even if paid off immediately with minimal interest charges. Because they collect the merchant's servicing fee, and don't experience default losses.
As usual, the populist crapstorm directed at "usury" rises exactly when the masses are sticking their bankers and robbing them blind. Not the other way around.
Then there are those of us that pay it off in full every month...