Seriously though, why is that the case? If she's a public servant, she could donate her time to talks easily. When you're being paid that much money to speak, then are asked to sit in judgment on this company, are you really expecting her to bite the hand that feeds her? *At the absolute best it puts her in a terribly awkward position. At worst it's bribery.
This amounts to an argument that people can't go back and forth between the private and public spheres. To be fair, this is something some people believe, and was very visible in the case of Ajit Pai outrage. But if that's what we're saying, let's be clear about it.
I just also think they should recuse themselves from an investigation when those whom they've had significant dealings with are being investigated. $700k for 3 speaking gigs, we're not talking about a CEO she had lunch with one time, there is a significant business relationship there. That relationship might not affect Mrs. Yellen's judgment, but if she doesn't absolutely drop the hammer on Citadel it at least looks like bribery. The very fact that the question is raised is the problem.
Or I suppose you could say that anyone who has held a government position, left it, and then ever made money in the private sector is ineligible for future government work. In effect all this does is just bar past officials from being elected again. This again reduces the pool of qualified talent by a lot. Janet Yellen is probably the most qualified person in the country to be the fed chair, it seems like she should be allowed to imo.