I wouldn't say "impossible", just, "very unlikely". Needing cash in hand is only an issue if you need that cash to buy things right now, like food. We could get problems if something happened that shut down our electronic banking over a very wide area (like all of North America, say), but in that case, the catastrophic event that caused that shut down would likely overshadow the problems caused by a lack of physical cash.
Well, the control structure is partly legal, in that banks are quite heavily governed and audited, and just making money bits appear out of nowhere would be found out quite quickly, and partly pragmatic self-interest, in that banks monitor their interactions with other banks, and also with their customers, to ensure they don't end up holding the bag if/when a fraudulent transaction is made/discovered.
As an example of the latter, my bank allows me to make deposits via banking machines, and credits that amount to me immediately. Based on my history of banking with them, they trust that I'm actually depositing what I say I am depositing. So I could, in theory, make a fake deposit, and then immediately withdraw money from my account, thus effectively stealing it. However, that would be discovered as soon as they actually checked what had been deposited in the actual machine, and they would take action against me - by freezing my account, debiting the amount stolen for what money I really have on deposit, and/or reporting me to the police for fraud.