You don't need a credit card for this, in principle. But, given that credit score is a thing in US, and that buying things with a credit card and consistently paying the balance off increases it - but no interest accrues until the end of the cycle - it creates a strong preference for credit cards in practice.

I do agree though that in practice this (pervasive use of credit cards) is one of the major contributors to indebtedness. Because you don't have to pay off that balance entirely, it becomes a psychological trap for too many.