Geeking out on this application of analysis-meets-Star Wars by Seth Masket of the University of Denver Political Science Department :
It is a bad idea for a republic to outsource its police and military power, as well as most of its diplomacy, to an autonomous religious cult. Monopoly on the use of force is a central function of a healthy state. The Galactic Republic relied on the Jedi to enforce its will domestically and internationally. Such a scenario made the republic very vulnerable to a Jedi coup, something senators would have been aware of and vigilant against. The Senate was insufficiently vigilant against a rising Emperor Palpatine because its main fear was an Emperor Yoda.
An earlier post on the lack of minority party was also clever.