The incentive for merchants to accept cards for payment is that it'll increase number of sales. And it does. In principle this should even out over all sales.. but cards do make it easier for consumers do purchase stuff, and I'm absolutely sure that I personally spend money way easier with a card than without (not that I spend more than I make, mind). The total number of sales go up.

I haven't used cash in my home country for the last two decades, at least. I mean, CC works even on parking meters when paying half a dollar (equivalent) for a few minutes of parking, and I can use a card in flea markets and even some garage sales.

Oh, I forgot: A lot of shops, restaurants, and other establishments have stopped accepting cash, even if it's illegal to do so (legal tender etc). That's because handling cash costs them MORE than handling credit/debit cards. In other words: It appears that using cards LOWER the costs for the merchant, not the other way around.

EditAdd: I presume a lot of the cost saving is that paying by card is 100% electronic, just tap the card (add the pin code if it's expensive enough), and the transaction goes directly into the shop's account. With cash it's way more cumbersome. Way, way more.

(Mind, there's no such thing as signing by hand anymore. If there were paperworks involved it would be different. But there aren't any, not in Europe and not in Japan anymore either)