coil resistor

No, they way they work is they drop the coil voltage to approximately the same voltage that the system sees during starting, so that when you are starting, and BYPASS the ballast, you have a hot spark

They are called a ballast because they change temperature with current to "even out" current draw. As the ballast gets hotter from more current, it's resistance goes up, tending to "slow down" current flow.

There are "straight" 12V coils. The original HEI is such an example....operates without a ballast. Many industrial engines tractors and so forth use full voltage coils with no resistor

Of course discharge ignitions such as CD, MSD, etc do not run DC current through the coil. The ignition feeds a pulse to the coil, it is "just a transformer", so these systems don't use a ballast, either