Here in Brazil, we have that since last month. The new money transfer system (Pix) allows anyone to send money to a key, which can be a person's CPF (the tax ID number nearly everyone has), a phone number, an email, or a randomly-generated number. These all map to a bank account (you can also use Pix to send directly to a bank account number); the directory with these mappings is kept by the Brazilian Central Bank, and the mappings are inserted by the participating financial institutions.

So assuming my email was [email protected], and I had asked my bank to map the Pix key "[email protected]" to my bank account, anyone could "send cash" through Pix to my [email protected] email; the cash would arrive at my bank account nearly instantly (even during weekends and/or holidays).