1. They're too small.
2. They're not totally random. The attorneys are allowed to eliminate members of the pool.
3. The jury doesn't actually run the trial. Nor do they run the police department, for that matter. The trial is run by the judge and the attorneys. The jury is mostly passive listeners. They're spoon-fed info at the trial and not even allowed to know all the facts.
4. Jury terms are too short. Contrary to what the previous commenter suggested, it's not ideal to have short terms. Citizen legislators should probably serve 1 or 2 year times. They need time to learn how to do the job. They probably need preparation before they take the job.
This is election as per 18th century Britain elections by the propertied classes.