Expert's answer

The K/W Call Letters in the United States write up by Thomas White provides a pretty comprehensive overview of the call letter assignments and breaks it down state by state. Wikipedia also provides information about the history of the call sign assignments.

Many of the stations with the "wrong" first letter in the call sign are simply old enough to pre-date the creation of the rules in 1912 and/or the shift of the boundary from the Texas-New Mexico border to the Mississippi river in 1923. Some stations obtained their out of place call signs by making special requests. One example of that is WACO FM in Waco, TX. Today new stations are typically required to adhere to the W/K split at the Mississippi.