They're usually ordinary flyback systems, just like points systems. I never saw a CD multistrike system, but that was long ago, when every CD system was triggered by an SCR, a device that can be turned on but not turned off. But since then, high voltage, high current devices that can be turned off have become more common, so multistrike CD should be easier to implement. I had a double-strike CD system that consisted of 2 separate CD units because I didn't know how to make anything better.
True, thanks to the EPA and its stringent emissions standards that include cold weather, cold engine conditions.