I think you need some basic classes on electronics. Maybe the Art of Electronics is a book all have to read first.

That picture shows the relation between Current and Voltage. Do you notice how steep is the curve at the point where the diode starts to contact? A very little increase at Voltage and the current will be infinite!. Thats why a resistor is needed or even better a current source to stabilize the current at 30 or if you insist on decreasing ED life at 50mA.

A battery is very constant and 12 will never be 13 volts without any good reason. But Power line? No ones guarantees the 240Vac. So what will happen to you precious diode (read LED) when the voltage across the pins moves away from the knee of the curve? Bam!

Ioannis