I was at someone's house once and they made a phone call and had someone bring $50,000.00 cash to their home from one of their bank accounts. I think the person worked for the bank and wasn't a relative with their name on the account.
Many services are available to people who are wealthy enough to use private banks. The linked Wikipedia article says:
...banking services (deposit taking and payments), discretionary asset management, brokerage, limited tax advisory services and some basic concierge-type services, offered by a single designated relationship manager.
Having cash delivered to your door would come under "basic concierge-type services".
This is a facility called Home Banking, which banks in some locations offer. You do not necessarily have to be super-rich to use it though.
Kotak Mahindra Bank has been offering it here in India for about 10 years now. Other banks have followed suit with similar offerings.
I am not super-rich or anywhere close1, but I have used this facility occasionally when I couldn't visit an ATM or the branch, to either get cash delivered to me, or to deposit cash into my account.
The banks do charge a convenience fee for this facility as you might expect, but they waive it off if your average monthly balance exceeds a certain amount.
Not sure about how it works in other countries, but here in India, if you have an account with one of the top customer-friendly banks, this facility is as mundane as a cheque book or a debit card.
1 If I were, I probably wouldn't be posting here. ;-)
Anyone who has that kind of money to blow probably has a CPA with a power of attorney who could provide such a service.
I don't have that kind of money but I do have a CPA with a POA who would gladly charge me and arm and a leg to deliver money to me.