Citizens United is not the problem, Buckley v Valeo is. That was the case that legalized bribery by claiming that campaign donations have first amendment protections – that “money is speech.” After that, the only barrier oligarchs had was campaign contribution limits, which Citizens United offered one way around.
If Citizens United is overturned but Buckley v Valeo left standing, bribery and corruption will still be legal and all oligarchs will have to do is find another way around contribution limits. The focus on Citizens United and “corporate personhood” is a distraction from the actual source of what is happening.