Before I answer, are you seriously arguing that taking a job as a professor is the same as getting paid 1 million dollars for ~10 hours of work?
The debate seems to be over the price. $700k / yr from lecturing to hedge funds is bad but $150k / yr to do the same at Harvard is good?
(2) Her salary is in line with others in her position and is given in exchange for doing actual work.
(3) Harvard is not in a position to directly profit from potentially privileged information leaking out in her lectures to students
(4) Harvard is not in a position to directly benefit from Yellen influencing current government regulators/policy makers
(5) Harvard is not in a position to directly benefit from Yellen taking a subsequent regulatory/policy position in government
They don't? Harvard's $40 billion endowment is larger than Citadel's assets managed. Harvard is a hedge fund that does education as a side hustle.
Is a position as a lecture of Economics at Harvard considering working for personal profit? Writing books on subjects that they are experts in? How about writing for the NYTimes? Appearing on TV? What about if they did all those things before taking a government job?
If your answer is yes to those things, then taking a high-level government position becomes impossible for anyone working class. Since you believe that the position bars them from any worthwhile future employment, they have to be independently wealthy before entering government service.
I personally enjoy reading the works of Ben Bernanke and think that he should be allowed to continue his work in economics despite having held a top position at the federal government. He's intelligent, insightful, and a good teacher.