If we picked our government at random from the citizens things wouldn't be as fucked up as they are today.
Agreed to a point. There are something things that wouldn't be good though. I don't want Joe, never graduated from high school and still works as a Cashier at McDonald's at age 35, to be one of those people. There should be at least some reasonable standards for who would get chosen.
Only because some citizens do everything possible to not get on a jury.
There is a way around this that I think is reasonable (although I'm sure there are many that will disagree with me). You make it mandatory that a business pays the person who's on the jury his/her full wage for the duration. You could still allow some special provisions for really long trials (more than a week). Considering how rarely people get called (about 5 times during your adult life) it's not all the inconvenient and if everyone has to do it then it's not much of an extra burden to let an employee take time out to do their civic duty.