You may never burn out the points with full voltage if you don't drive very often. The resistor wire or ballast was added so you could drive thousand miles on a set of points. The resistors would knock down the voltage to around 9 volts while running to extend the life of the points, but they all had a bypass during starting so they would receive full battery voltage. The higher voltage was to aid in cold starts, but due to starter draw on the system, the ignition still didn't get full battery voltage.
On my distributor machine, I check with full battery 12.6 volts, you can hear the difference in the spark when I add in a resistor. I have 8 plugs mounted so I can test cap, rotor, and wires, plus I can see the color of the spark at the plugs.
Your problem sounds like a carb issue, or old fuel issue. Sooty plugs is the give away clue. With out a resistor in the ignition system, the plugs should be running clean with the higher voltage spark.
