The Supreme Court knew when it decided
Citizens United that the only way the decision would work is if there was a robust system of disclosure. Reasoned the Court, there should be no problem with unlimited election spending so long as it's clear who's paying for it.
And those were the conservative Justices, Greg. Well, at least four of them - Thomas thought disclosure requirements were unconstitutional, too, but there were eight Justices who disagreed with him.
Justice Kennedy, in the Citizens United opinion, wrote:Disclaimer and disclosure requirements may burden the ability to speak, but they “impose no ceiling on campaign-related activities,” Buckley, 424 U. S., at 64, and “do not prevent anyone from speaking,” McConnell, supra, at 201 (internal quotation marks and brackets omitted). The Court has subjected these requirements to “exacting scrutiny,” which requires a “substantial relation” between the disclosure requirement and a “sufficiently important” governmental interest.
He also illustrated a history of cases where, even Judges wanting to overturn spending caps didn't want to overturn disclosure laws.