The flaw in your logic is that if you don't power down long enough, the RAM doesn't get fully wiped and the device never initializes, so it never gets a chance to wipe the RAM. Technically, the statement is wrong - a program never assumes RAM is "wiped". It always writes the data values it expects to find later in RAM, whether it's numbers or all zeros.
But that's not the real reason for waiting to re-power a device. In actuality, there is a small reset circuit in microprocessor devices that detects when the power supply increases and reaches the correct voltage(s), then sends a pulse to reset the microprocessor.
If you don't power down long enough, the voltage stays high enough that the reset circuit never detects an increasing voltage and never sends that pulse to reset the microprocessor. At that point, RAM could have become corrupted from the power outage and/or the microprocessor just starts running from a random place in memory because it was never reset. That's enough to hang the device.
There is no standard defining how fast a power supply should drop it's voltages to zero, but us technical folks know from experience that almost all devices will have fully powered down after 30 seconds. That's really a bit of overkill (longer than necessary) for many devices, but there is no better way to be reasonably sure that any one given device will reinitialize properly.
That's the real reason why powering down and waiting 30 seconds before powering back up has became a rule of thumb. That half minute can seem like an eternity, but it's much faster than waiting 10 or 15 seconds, powering up, figuring out that the device has hung, then powering back down and waiting the full 30 seconds after all.