On that point, Congress cannot "set things up as it sees fit." The constitution goes to great lengths to create a complex, three-branch system of government with specific powers allocated to each branch. Anytime Congress creates something new, it has to fit it into the three-branch model in a way that is consistent with the principles of that model. It's like a "pure" microkernel in computer science: there is a framework that dictates what goes in kernel space versus user space. Except with the constitution, the structural principles are legally binding. You can't delegate executive functions to mere employees of the legislative branch, just like in a pure microkernel you can't put the GUI into the kernel.
In this case, the DMCA creates civil and criminal liability. Creating exceptions for that is the exercise of a quintessential executive power--enforcement discretion. That power must be allocated to an executive-branch agency.
If you concede that it looks like an executive agency then it actually seems quite proper that the executive control it.
I can see how someone might disagree with that for various reasons (see the article) but in context "if it looks like an executive branch agency, then the Executive branch should have control over it" seems like a great argument and one that would probably carry in Congress, they have tended to put executive agencies under control of the executive in the past.
no more major questions doctrine