If the problem is that some people don't have a checking account, wouldn't it better to provide them with a cheap/free checking account? Even if all local shops accept cash, there's still tons of stuff you can't do without a checking account. On the topic of cash-free living: I only use cash for 3 things these days: to buy cheese, to pay my cleaning lady, and for my son's weekly allowance. Even the babysitters accept…
I don't know about everywhere in the world, but aren't most 'checking' (most people don't use checks any more) or current accounts already free? They make money off investing your deposit. How much are people paying for their current accounts?