The US technically even has laws that that were supposed to do that still on the books. A particular problem was a very broken decision by the US Supreme Court in Citizens United v. Federal Election Commission [1] that opened too large of a barn door that the US has been reeling from ever since. That trial argued that companies were individuals/people and that money was the "free speech" of companies and shouldn't ever be curtailed. So there are so many things wrong with that court case on so many levels. It led to the rise of Super PACs (Political Action Committees), companies designed to launder money for political gain where the donors are allowed to remain anonymous and the Super PAC "speak" for them, because now it was "free speech" and not bribes and regulatory capture.

I know pessimists that believe the only way the US succeeds in the Campaign Finance Reform it needs now is through a Constitutional Amendment and if we can't count on Congress to be interested in it (due to bribery), and not enough individual States seem to care (some because they want a chunk of that pie), it's going to take a full Constitutional Convention to pass that amendment, something that hasn't successfully been done in the US since 1787 (also, the first attempt).

[1] https://en.wikipedia.org/wiki/Citizens_United_v._FEC