The system more generally prone to corruption is obvious. Even by Chait's logic -- Obama is unusually honest, and GOP presidencies devolve into patronage operations -- we're likely to see more patronage than honesty in the near future, when the machinery of redistribution so carefully built by Democrats falls into the ideological descendants of the people who executed the K Street Project. By Chait's own logic, his preferred system will only work when Democrats are in power.
The actual nature of our two-party system, where Republicans and Democrats both regularly end up in charge, is that some unfair elite gains accrue to Republican interest groups and others to Democratic interest groups. (Some groups have bought off both parties.) If it were true that only redistribution can improve the lot of regular Americans, it would make sense for Democrats to ignore the illegitimate gains won by the people who help to keep their party in power.
But it isn't true. Regular Americans would be a lot better off if the worst rent-seeking were reined in, including rent-seeking by Democratic interest groups. As a matter of public policy, there are a lot of reforms that two smart guys like Wilkinson and Chait could agree on as discrete improvements. The obstacle is the contours of coalition politics in America even more than substance. Luckily, some people are trying to change the contours of coalition politics in America.
They should be encouraged.