The Dictator’s handbook is a good book.
Under the “rules for rulers” proposed in the book, Kaladin would not be a good candidate to lead the radiants. Currently, the Knights Radiant and Alethkar are one in the same, as the Alethi center of power is also in Urithiru, and most of the Radiants currently gathered are loyal to the Alethi ruling house. To rule, Kaladin, or any other successor, would need to take control of the keys to power, who are the Alethi generals, high princes, high lords, and ardents. Kaladin, while technically a light eyes while using the Syl blade, is still socially a darkeyes. He also has forged no political relationships with the keys to power. He would replace hem, and they know it. The Alethi armies could destroy the bridge men, and as Dalinar reminds us, Shard Bearers can’t hold ground.
Jasnah would be a much better candidate to seize power, because she has legitimacy, connections, and political savvy. The Highprinces probably trust her more than Dalinar. Of course, she’s already number 2 in the Alethi/Urithiru power structure, and I don’t think she wants the power. Remember, while these rules apply very well to real politics, they don’t apply in a fictional world unless the author wants them to.