That is why I said it was similar to a trial-by-jury. The jury isn't versed in law or in the details of the case, so they get all the information they need to make a decision from the lawyers presenting the case. That leads to situations like one we had in my home country: A woman was sentenced to life in prison for a murder without any evidence. None at all. She had motive and was 'an asshole', and that was enough for the jury to be sure she did it.
If there was a way to objectively give them the facts of the case and the knowledge they need, the system would be perfect, but unfortunately that's not possible. And until it is, i would rather have people making decisions based on their own badly informed opinions than people making decisions based on others' opinions with a veneer of legitimacy.
There is the question of writing laws in the appropriate legalese. In practice, at least in France, most laws come from the executive branch, and the Parliament examines them in a commission, "patches" them by adding amendments, and votes. I'm sure the legalese part could be taught or handled by specialists. Apart from that, I don't see why it would function in a worse fashion that what we currently have.
In the case of a randomized group, that power isn't with the group, it's with the people who educate them on the matters and who frame the issue. There are a million ways to present any matter, and none of them are objective. You're putting the power to influence and even determine a nation's decisions in the hands of the experts that inform them, rather than the randomly selected people. It would become very efficient to buy those people instead of the voters.
The problem of the matter isn't whether it would function worse. The problem is that it would function less transparently. It would ostensibly be a fair and completely unbiased system, but that could be manipulated behind the scenes in far more insidious ways. That's very dangerous. Personally, I would rather have a more unfair but more transparent system.
Whilst theoretically not having any inclination towards achieving a particular outcome is a distinct advantage in the latter situation, I can't see how that's the case when it comes to actually governing.