We use it because juries can't write laws, enter judgements, or execute laws/judgements, or, really, do anything on their own. They serve -- particularly in the criminal sphere -- as a brake on government.
Which might be an interesting role in this case. Any time congress tries to pass a bill, it not only needs the President's signature, but it also has to pass a randomly selected panel of ordinary people?
Why not move to popular vote for laws? Some people think it can be hacked/gamed, but --if that's the case so can any normal election - and a lot of times republicans will do anything they can to get people not to vote because the more voters that show up, the more likely they are to fail.
I really like the idea of Liquid democracy -- what if a new political party popped up, and the runners agreed to take a public poll before every vote and the party can choose to keep or throwout the candidate at the next election based on how often they side w/ the people.
Throw in location/regionalized grouping, and you can easily have all sw ohio voters contribute to reps vote tally from that area...etc..
Also what if we raised the bar on representation - We currently have 1 congressmen per million... that's highly not representative.. -- true representation needs to also find a way to not only represent locations...but also demographics better..
What if we just tripled the reps, but required 1/3rd come from middle class, 1/3rd from lower-class, 1/3rd from upper class.
It would provide a better idea of what the people really want from all levels.
An ordinary popular vote for laws I don't like because I don't have time to research everything to the depth I would need to. Something like liquid democracy suffers much less from that, of course. I've recently been taken with the idea (though I am not at all convinced it would actually be a good idea) of drawing panels at random - like jury selection - to decide individual issues, but giving them time and pay to inform themselves and deliberate. Just expecting people to come to well informed decisions on their own time doesn't turn out great.