It is interesting to what extent executive and judicial power were connected in ancient Israel.
Early on, "Judges" such as Devorah and Gideon gained their repute primarily as political and military leaders.
Later on, kings such as Shlomo were expected to serve as the highest judicial authority, most famously with the two mothers and the splitting of the baby. This unification of judicial and executive functions seems therefore to have survived the political transition from a loose tribal confederation to a centralized kingdom.
Indeed, R' Eliezer Berkowitz argues that the word "lishpot" in Tanach did not have the same connotation of impartiality that it carries in modern society. I would think its meaning is closer to "to protect one who is in the right from one who threatens to do him harm". The moral judgments from which the judge's attitude proceeds must be impartial, but once it's clear who is in the wrong, the judge's main task is to take the side of the victim and ensure that the injustice is prevented or redressed. This can mean fighting wars, or it can mean enforcing a legal ruling. Either way it is called "judging", and either way the focus is on action not intellectual contemplation.
I may idly speculate that unifying judicial and executive power increased the standing and power of the judicial authority, while simultaneously increasing the risks if the judge/ruler was corrupt. I think the necessary safeguard in the Shoftim period was provided by the judge's dependence on public approval. Once the monarchy was established this method became ineffective. Therefore the prophet had to assume a more significant and constant public role.