That only solves for explicit quid pro quos. It does nothing for the case where corporate sponsors donate to candidates who honestly signal during campaigning that they are the kind of candidate who cares about those sponsors' interests.

I think explicit quid pro quo is far less impactful/prevalent then pro-corporate donors simply looking at the pool of campaigners and putting weight behind candidates that look like they'll vote how the donors want. All that requires is for the donors to be able to at least partially predict future behavior from candidates' current appearance. Secret votes won't change anything on that view.