The thing is that bribery is technically illegal. Of course it's completely ubiquitous, but it's generally (FFS Menendez) done in a nuanced and practiced way. Newcomers are not always going to be willing to accept bribes, and actually trying to offer them one would require much more overtness, which enters rapidly into the domain of clear criminality, to say nothing of when your bribe attempt is rejected. And these are the issues with just one guy - with hundreds of politicians regularly cycling in and out, this scale of bribery is just not realistic.

The bigger risk with sortition is that power isn't granted through a title, but through people agreeing to respect that title. If the authority of that title ends up being undermined, then it's entirely possible for power to shift from our representatives to other, probably more entrenched, groups. One could argue that on many issues this is already the case. For instance Congress ostensibly has oversight over the intelligence agencies but the power relationship there is completely reversed. For those that don't know, Congressmen don't have classified access by default. Millions of people in the US have classified clearance, but the people representing the country at the highest level - nah, why would they need such a thing?