All my friends could come up with when I suggested the idea were:
"ATMs are convenient enough, and even ATMs with fees would probably be cheaper than whatever you'd have to charge for the service"
And:
"And people primarily need cash when they're out, not at home"
But isn't it true that you really shouldn't underestimate the laziness of people? People will gladly (and perhaps subconsciously) pay a little more for a service that they really find convenient (Uber). And the 'drop off' doesn't have to be at your home, it can be at most public addresses depending on the city that you're in.
As far as security goes, there could be multiple steps, but the easiest (and really the only necessary one) would be that when the person that drops off the money arrives, he/she has to first check with the recipient; their ID and credit/debit card, or other verification like that. Then give 'em their money. That's it!
I'm not talking about the hard parts, which is getting banks to work with you and so on. I'm talking about strictly whether or not this is a great idea with a market audience waiting.
So, please school me!