I think the idea of randomly selected government members is terrible - I feel democracies strength is in that it comes the closest of systems tried so far to approaching a 'meritocracy with strong incentives to work towards making things better for the people of the country'. And while it doesn't do well at that in many ways, it does better than the alternatives.
A randomized system of service would mean people who are both incapable of executing improvement (in all likelihood) and simultaneously lacking any incentive to do so. It would be a disaster.
In my system, you'd have people working to hire the best person for the job, who knows if they want to keep doing the job they're going to get a "review of their efforts" by the next group, a sampling of the nation at-large. They know that they won't be able to avoid tough questions, not easily.
Bribery and kickbacks are possible, but, assuming the final vote was secret, I'm not sure how likely it would be - it doesn't seem like the incentives would line up, especially if there were severe penalties for getting caught accepting such bribes from the get go, especially if there were rules saying that they could vote on modifying the rules of the assembly, but only a future assembly could benefit from them. While each individual might wish to accept bribes, they would know the rules are strict - they are also not inclined to let other people accept bribes and make the original person worse off, so their unlikely to move to lighten the prohibitions. With a secret vote, even if they accept the bribes they have no incentive to actually vote for the candidate they promise to vote for - if they were honest and trustworthy and likely to make decisions based on moral loyalty, they probably wouldn't be accepting bribes to begin with.
Every incentive indicates a group that is significantly less likely to take bribes than our current congress - and who, if convened to elect members of that congress, are more likely to uncover evidence of such bribes and penalize those who accept them.
We already trust the people to select an effective ruler - My proposal mostly involves building a system that best equips them to do just that, in the most realistic way possible.