This is just not true. The "revolving door"-system generally refers to the problem that private firms (the regulated) employ people who formerly worked for the regulator, thereby incentivizing regulators to regulate in favor of private firms so as to maximize their job prospects after their government term has ended. While it is true that candidates for governmental positons get temp positions at think tanks, think tanks themselves are neither regulated nor get paid by regulated firms to lobby the regulators to propose beneficial (to the regulated) regulations. So neither Cato nor AEI nor Brookings are part of the revolving door system.