This is a pretty one sided account. The CFPB didn't spring into existence because some unelected bureaucrat decided it should exist. The structure that the DC Circuit Court of Appeals found unconstitutional likewise wasn't the design of some unelected bureaucrat.
The Federal Arbitration Act is not the only piece of duly enacted legislation in question here. Another peice of legislation -- one that was passed by both Houses of Congress and signed by the President of the United States -- was the Dodd–Frank Wall Street Reform and Consumer Protection Act.
A lot of bankers and their lawyers fought against Dodd-Frank tooth and nail. They were very happy with how things worked up until that point, thank you very much. Normally the American public doesn't have the attention span to thwart the bankers' lobbyists -- they are in there 24/7 lobbying for narrow concentrated interests and public interests on the other side are too diffuse and abstract to mount an effective defense. But in this case the stars aligned and legislation was passed. So the lobbyists moved on from stopping the bill from being passed to killing it afterwords in the regulatory process.
Where were the impassioned speeches about separation of powers and the will of Congress when bank lobbyists were busy eviscerating the skin-in-the-game rule?
Sure, Congress has every right to pass a law, which is what they did here, and override a prior law. But by the same token the Dodd-Frank Congress had every right to override the Federal Arbitration Act. This isn't a question of separation of powers, it's a question of public policy. Congress didn't stand up for Congressional prerogatives, they stood up for banks.