Yes, running a higher resistance coil is always safer for the coil and ignition because of lower current, but it's not necessarily safer for the engine if using that coil causes the spark to fail.
And so yes, the potential downside is weaker spark or failed spark.
But this is not to say higher resistance coils necessarily produce a weaker spark. It's because the available dwell time might not be sufficient for that particular coil to charge fully to produce a strong spark. In fact, higher resistance/inductance coils may produce more spark energy than a low resistance/inductance coil, depending on how much dwell is provided.
Dwell time is the time during which the coil charges up with energy.
Dwell angle (in a Kz) is the number of degrees of crank rotation during which the dwell is active.
On a system like points or the Dyna S, the dwell angle is fixed, so the dwell time varies with RPM.
Higher RPM has much less dwell time than idle. Idle has very long dwell time.
A coil that charges quickly will usually have lower resistance and lower inductance.
A coil that charges slowly will usually have higher resistance and higher inductance.
So when we talk about the resistance of a coil, we are using that to also imply the inductance of a coil, and thus we are really talking about the ability of a coil to charge quickly or not.
If you have a very long dwell, you can use a "slow" coil and get plenty of spark energy.
If you use a "fast" coil you will be in danger of melting the coil or the igniter. The extra dwell time only translates to heat generation in the coil and igniter, not extra spark energy.
If you have a very short dwell, you will need a "fast" coil to get plenty of spark energy.
If you use a "slow" coil you will likely have weak spark or fail to spark at all, especially at higher RPMs.
So as in most things, it's about finding the proper matched combination of parts.
The Dyna S was designed as a replacement for points on motorcycles which typically have very long dwell compared to a car. This is why motorcycles with points came with "slow" coils. Here I mean anything 3 ohms or higher as "slow". The Kz's with points came with coils that were basically 4 ohms. The Dyna S nearly doubles the dwell time compared to points (on a Kz), so the dwell will be far more than adequate for 4 ohm coils and even 5 ohm coils. And since Dyna designed it to handle the current of a 3 ohm coil, you have many options available. There is a chance that 3 ohm coils might give better spark at very high RPMs, but then at idle it will be very inefficient and may drain battery power and generate more heat. It's a tradeoff.
Some people use the Dyna S with 5 ohm coils and have never reported any problems.
Some people use the Dyna S with 4 ohm, stock coils and have no problems as long as the coils are in good condition (not too old).
Some people use the Dyna S with 3 ohm coils and have never reported any problems.
A very small number of people have reported charging issues when converting to a Dyna S and 3 ohm coils. Of those, more were '78 and '79 Kz650 owners than any other Kz, though it has shown up on a tiny handful of other Kz models.
Often the fix was to convert to 3-phase, or use a stock ignition system. The stock Kawasaki Kz electronic ignition is far more efficient than the Dyna S, and thus uses less power. Most people opt to convert because it's getting harder to find good, working factory ignition systems for Kz's.
So to answer Mikaw's question:
Cars with distributors have very little time between spark events to charge a coil because that single coil has to fire multiple times for every crank revolution. To do this they need a coil that charges fast. Typically they would be in the 1 ohm range, but could be lower or slightly higher. But as mentioned, this is not exactly safe because at low RPMs, the extra dwell leads to heat in the coil and reduces longevity. The extra current also greatly reduces the life of the points. The classic solution is to use a resistance-changing ballast resistor, and a special circuit during startup to bypass the resistor.
Well, this is not easy to implement on a kickstart motorcycle since you are not turning any switches while kickstarting. So to eliminate the distributor, and simplify the circuitry, they decided to just use two slow coils. This eliminates overheating issues and ballasts as well. So Kz points systems use 4 ohm coils and this is a good match for about a 180 degree crank rotation for dwell. This also gives good points life by having such a low current. The 4 ohm coil still charges fast enough to give good spark up to about 10,000 RPM.
When Kawasaki designed the electronic ignition, they figured out they could save some power, and also eliminate crosstalk between coil circuits by reducing the dwell to about 100 to 120 degrees. This required faster coils. The best match was found to be about 2.3 ohms. When their first system came out, the coils were not available so they used much lower resistance coils and added a resistor to make up the difference. That is why some Kz1000's had ballast resistors. They can be eliminated when the coils are replaced with 2.3 ohm coils. So that is why we have 2.3 ohm coils or a few, rare 1 ohm-ish coils.
Dyna decided to make 5 ohm coils as replacements for points coils. In order to not burn out points on bikes that use long dwell, they made them 5 ohms, but they work pretty well in place of 4 ohm coils. They had to make a single coil to fit on various makes and models, so there is always a compromise with that.
Then Dyna also makes 3 ohm coils which work on the Kz electronic systems and will also work for the Dyna S. Again it's a single coil to fit a wide range of uses, so that's why it exists.