Basic speeding at epsilon over the legal set point is hardly worth taking a license for. Especially when such values are often set arbitrarily.
Consider also that any three strike system will impact people who drive more miles more often. So a population of more reckless but lower mileage drivers will be impacted similarly to high mileage drivers going speed limit +/- noise.
There are a lot of other factors that are stronger signals than the first order approximation of time behind the wheel. E.g., professional drivers get more practice and probably have fewer accidents per time or mile than casual drivers; some people look at their phone or in-car computer while driving and others don't; driving around pedestrians and bicycles is more dangerous to society than driving in times and places when the roads are empty or only have other cars (interstates); etc, etc.
Anyway, I suggest looking at three-strike drug possession laws as a good example of how dysfunctional this kind of hard-on-crime legislation is in practice.
Consider also that any three strike system will impact people who drive more miles more often. So a population of more reckless but lower mileage drivers will be impacted similarly to high mileage drivers going speed limit +/- noise.