> it’s always going to be possible that that company simply liked how the representative did their job and hired them
There's actually no reason why the voting record of a citizen legislator needs to be released to the public. They do it with elected officials, because if you're going to vote for someone, you want to know how they voted. But with unelected officials, it could be secret ballots, so nobody even knows how they did their job.
> they like the PR of hiring ex-reps.
There's no PR in hiring a randomly selected person who was only in office for 1 year. Nobody even knows the randos.
> or any number of reasons a lawyer could bring up in court
Which reasons? All of the reasons that exist now relate to politicians having long experience, connections, and other things that go along with having a "career" in politics. None of the reasons hold for what is essentially a temp job.
> I think you’re confusing “representatives” with “elected representatives”. they would be representing the population at large
No, I'm not confusing anything. Getting randomly selected from the public is not the same as representing the public. An elected representative is expected to get the opinion of and serve their constituency. There's no such expectation in sortition. Compare with juries. A juror is mostly randomly selected from the public but doesn't "represent" the public. A juror doesn't need to consult the public about the trial; to the contrary, jurors are not even allowed to consult outsiders about the trial. A juror simply decides the case base on its merits and nothing else. There's no representation.
I think you're underestimating the inherent corruption of the current political system. By the time a politician takes office they're usually a "known quantity", because (1) they have to run an election campaign to introduce themselves to the public, and (2) in order to finance such a campaign, they have to raise money, which mostly involves going around begging wealthy interests for money. So such interests can already develop a relationship with the candidate before they get elected, by contributing money to their election campaign. Running for election is inherently corrupting in that way. Whereas government officials randomly selected from the public are wild cards. You can't just go around bribing a thousand unknown random people, because while some may take the bribe, the chances are decent that you'll run into a honest, ethical person who won't take the bribe but rather turn you into the authorities, and then you'll go to jail, because bribing a government official is a felony. All it takes is one honest randomly selected citizen to blow up the entire bribery scheme. So it would be massively dangerous for the briber. It's difficult to build "trusting" relationships with such short-term unknown legislators. This is why most political bribery takes the form of legal campaign contributions, which pose no danger to the contributor and are quite effective at getting results. Eliminate election campaigns, and you've eliminated the primary source of corruption.
We have to compare sortition against the current system, not against some ideal of perfection. If sortition is simply less corrupt that the current system, it's a win. You can always think of ways to game any system, but our current system is practically designed for corruption.