It is highly unlikely this is going to happen.
No one claims they're people. The law lets them stand in as people so society can function. The whole "corporations aren't people" meme is myopically fixated on campaign finance, ignoring the much larger issues around this legal doctrine.
Can a corporation own property?
Can it own patents? Copyrights? Trademarks?
Can it be sued in court?
Can it file lawsuits itself?
Can it make contracts?
I don't think any of us would like the result of answering "no" to all those questions, yet those are the questions that the legal fiction of corporate personhood was invented to answer.
Should corporations have the same free speech rights as people? I can see an argument for answering that "no", as rich corporations may speak disproportionately powerfully. I can also see an argument for answering it "yes", in the sense that corporations are just people acting together, and collective speech should be just as protected as individual speech.
https://en.wikipedia.org/wiki/Corporate_personhood
Remember that whatever constraints you put on EvilCorp's speech are going to apply just as well to the Sierra Club, a labor union, or the NAACP. I honestly don't know if that's a tradeoff work making. Maybe it is.
I agree with your point about transparency.
Addings more laws tends to help the people who can afford lawyers.
You could look at simplifications instead, eg change the voting system from first-past-the-post to something like range voting, and candidate behaviour (and thus reacting to incentives) would completely change.