I think there's a law that all counties in Kentucky have to be a minimum of 400 square miles (those created prior to 1891 are grandfathered in), which would make the split you proposed impossible, especially as Campbell County is only 152 square miles itself. (again, Campbell, like every other existing county in the state aside from McCreary County, is exempt as it was created prior to 1891)
I would imagine all states that have provisions to let people form new counties without a legislative vote have provisions to keep there from being thousands of little counties.
In South Carolina, a new county may not include any territory within five miles of an existing county courthouse and must have at least 1/124 of the population of the State. The reason for the odd fraction is that it is a legacy of the days when each county was guaranteed at least one of the 124 Representatives.
Frankly in most places, consolidating counties rather than splitting off new ones would make the most sense.
