New study for the Institute for Free Speech:

Ten years after the decision, this report asks if such claims about Citizens United were correct. Did the Supreme Court’s ruling that corporations and unions can speak without limit and contribute unlimited amounts to
finance independent political expenditures increase the amount of corruption in our democracy?

We find no evidence to support this claim. A comparison of public officials charged with corruption offenses by the U.S. Department of Justice nine years before and nine years after the Court’s decision show a decline rather than an increase in corruption. Further, states that were most affected by Citizens United saw a larger decrease in corruption than states unaffected by the decision.

The report considers correlations not causation, and I think there are other explanations (such as this one) for the decline in corruption prosecutions.