Some establishments, often restaurants, advertise 'cash discount', often on the order of 10% or so. It's against the rules to price discriminate like that, but it happens around a technicality, since these establishments are offering a 'discount' and not exactly a different price depending on payment method per se. Effectively, paying with a credit card in these establishments mean the consumer bares the burden of the higher costs related to CC transaction fees. So CC transaction costs are not 'always' priced in for everyone. Except large retailers and things of that sort of course.
But yeah, most people use a credit card like a debit card. You spend, then you pay it all off at the billing cycle.
The other benefit are points or cash back. Why wouldn't you spend on your card if you get points for it? Also, less coins to deal with.
But not everyone is eligible for reward cards. So in some ways, the points system is set up to help 'wealthy' individuals, because only they qualify for these reward cards, in spite of the fact the retailer has to price in CC transaction fees for everyone with just one price. As always, the 'rich' get 'richer' in that sense.