The legislature also has only the powers enumerated in the Constitution. As "create independent agencies" is not one of those powers, it comes down to a matter of interpretation as to whether one of the powers granted to Congress implies the ability to create independent agencies. But once you enter the land of interpretation, it's, well... open to interpretation, and thus it's not unreasonable for someone to take issue with a certain interpretation.
Proposal: constitutional amendment granting Congress the power to institute independent agencies lead by independently elected officials directly responsible to the voting public and subject to Congressional impeachment.
For example, make attorney general an elected, independent position.