OK so I don't want to sound like a smart-arse but it amazes me how often people ask these same questions without anyone ever really talking about how it all works and why.
The basic theory is pretty simple and once you understand it a lot of other questions go away - so I am going to be brave and try to set out the basic stuff:
The number one thing to understand is Ohms law. Don't go all glazed eyes because it is simple honest so stay with me. It's this easy ------ Current = Voltage / Resistance.
OK so our cars have a 12V battery - so that's the start point for the voltage.
Now, things like coils and ignition modules (and points) can either handle 12V or not. But the thing to understand is that it is not the voltage that is the problem; you can put 12V across your face and you will hardly notice. The problem is the current the voltage produces. It doesn't produce much across your face because your face has a very high resistance to the flow of electricity (at least mine does and if yours doesn't then you should be on a medical forum and not here).
In simple terms, the current (measured in amps) is how hard the electrons are bashing through the component and the harder they go the hotter it gets. An arc or MIG welder makes a lot of heat because it makes very high current.
So, in an ignition system we have components which can only handle so much current or they get too hot. Points can handle less than an electronic module, but not much less (depending on the module).
Typically points will be OK long term carrying 4-5 amps of current, and some electronic modules don't like much more than that either. So in those cases the resistance in the circuit needs to be about 3 ohms (because 4= 12/3). If you don't get that then go back and read again.
The Mopar electronic modules, especially the OEM ones, appear to be able to handle quite a high current (maybe 8 amps or more). Imagine a 100 Watt bulb flashing on and off 250 times a second, it's quite a bit of heat.
Most stock style coils have an impedence (that's another name for resistance when you are talking about something like a coil) of 1.3 to 1.7 ohms. At a full 12V those coils would be running something like 7 to 9 amps of current and things will get too hot after a while. Even a tough stock Mopar module will be feeling the strain.
Enter the ballast resistor. On stock systems the ballast resistor is the same or about two thirds of the resistance (impedence) of the coil. That makes the ballast take a lot of the heat (literally) off the coil. As a result the coil only has 6-8 V across it and the current through it is lower (so it doesn't burn up).
As an example - if you have a 1.5 ohm coil and a 1.5 ohm ballast they will split the voltage equally between them and both take 4 amps current (since the combined resistance is 3 ohms). If you have a 1.8 ohm coil and a 1.2 ohm ballast the current will be the same (because the total resistance is the same) but the coil will have 7.2 volts across it (remember - current = voltage / resistance).
Why does it matter? It matters because the coil works like a transformer to multiply the original voltage into a much higher voltage at the plug. We need that very high voltage or the spark will not jump across the very high resistance in the air gap between the plug electrodes.
Because the coil works like an amplifier, if the original (primary) voltage supplied to the coil is lower, then the secondary voltage to the plug is also reduced. So, on a stock system where the coil could theoretically put out 30KV if given 12V primary it may only be delivering 18KV with the ballast resistor in circuit (because part of the 12V is being dropped across the ballast and not the coil). This is OK because the plugs will still fire at 18KV (if they are not gapped too big) and it allows an additional bonus feature:
Bonus feature - when the engine is cranking the starter is doing a huge amount of work and that robs a lot of power from the battery which means the battery can not maintain the same current/voltage relationship with the coil. This would result in a much weaker spark just when you need it most (on a cold morning). So, the stock system jumps the ballast which puts the coil under a direct 12V supply and delivers a better spark. As this only happens for a short period there are no concerns over exactly how much heat is being developed.
So why change anything?
Ballast resistors do give up eventually so if we can get rid of them that is one less component to worry about, however, the main reason people try to get rid of the ballast is to deliver a full 12V to the coil and therefore create a better spark.
If you have been following the foregoing you will now see why so many people change the system and then complain that the coil etc. got fried. For racing it is often OK to run a full 12V to the coil because the engine is not running long enough to build up the heat needed to cook anything. On a street vehicle this is not the case.
How to do without the ballast:
There are basically two ways to get rid of the ballast safely.
The first and most popular way is to fit an aftermarket (or fabbed) ignition system which cuts off the current to the coil once the primary winding is saturated (in other words it doesn't keep hitting on the coil after it is charged). The MSD, HEI and Pertronix II systems (and others) work like that.
This is the best option because it allows us to use a very low impedence coil at a full 12V. The full 12V gives the coil the maximum voltage to multiply and the low impedence means it gets there much quicker per cycle (so it maintains good spark better at high revs when the cycle is shorter).
The second way is to use a coil with a high internal resistance. As an aftermarket component I only know of the pertronix flamethrower 3 ohm coil. It is rated at 40KV secondary voltage. If you fit this without a ballast resistor you will still have 3 ohms in the circuit so nothing is going to get too much current whatever else is going on. Also, in theory, you should still get enough spark to fire OK when cold even though the battery will not be delivering 100% (although perhaps not if you open up the plug gaps too much). The downside is that the impedence will limit the systems capability to charge the coil fully when the engine is revving really hard. On a street car this should not be much of an issue.
Therefore - if all you aim to do is to lose the ballast resitor, you can keep the stock Mopar E I module, jump the ballast, and fit a 3 ohm 40KV coil, and leave your plug gaps as they are. You will probably not get better performance (maybe a bit).
Can we now have less questions about coils and ballast resistors ?
OK, probably not.