You can't just transfer money to a person that has no account. That's not an 'edge case' that just isn't how it works unless you want to use WU or something similar and even they have strict KYC requirements for larger sums.

If you want to move large amounts of money outside of the regular financial networks and oversight it is possible but (1) it will cost you (2) you will be breaking the law and (3) you may cause others to be breaking the law. Bitcoin would be one way to do it but even that is not nearly as anonymous as most of its users believe.

Banking is a regulated industry for a reason. There was a period (roughly until 2001, guess why) when banks were willing and able to bend the rules depending on who the customer was and how much money was involved. Those banks that continued to do this post 2001 have - if they're located in the West at least - had their ears bent in ways that they did not like one bit and even the Swiss now play ball.

Cash is becoming harder to use and harder to get. Money will most likely go digital in the West soon, the various governments don't like the unauditable and untaxable money streams that cash provides.