I thought the resistor only provided current limiting? Maybe you've explained but I don't get how it drops the voltage. I've used voltage dividers using 2 resistors, etc.
As before, Ohms law says that U=IxR, voltage = current x resistance. For a given current thru a given resistance there is a given voltage drop. The voltage drop across the LED is relatively constant (around 1.5V in your example). For a voltage drop of 5V across the LED the current would be in the tens of amps, instantly destroying the LED - provided the source could deliver that amount of current of course.

Also, when you say 'L.E.D.s aren't meant to be driven by a low impedance voltage source; isn't when a circuit using an L.E.D. for a power indicator (which I've seen) driven by a regulators output (to say power is turned on via throwing a switch in the circuit) a low impedance source?
The voltage regulator itself is a low impedance voltage source but surely there was a resistor in series with the LED wasn't there? That resistor turns that low impedance voltage source into a high(ish) impedance source, limiting the current thru the LED to whatever the designer of the circuit has decided.