Hypothetically, if Congress passed legislation saying "it looks like an executive branch agency, the Executive branch should have control over it" you'd consider that a generally reasonable position all else equal?
If you concede that it looks like an executive agency then it actually seems quite proper that the executive control it.
No. Congress can set up and modify different parts of the executive branch, but can also set up wholly independent agencies that are not parts of the executive branch. The current administration often argues (through legal filings or proxies) that such agencies are somehow illegitimate and the executive branch should have authority over everything. That idea isn't peculiar to this administration, they just seem to have gone all-in on 'unitary executive theory' because it provides arguments for consolidating as much power as possible in the office of the Presidency.
The current administration doesn't seem to be involved in this. This appears to be Congress, on paper, saying that the executive should control something that looks like an executive agency.
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.
An argument against could refer to established practices of limiting power of executive branch in particular...
youd also have to consider that the executive branch isn't allowed to make decisions, so the copyright office couldnt actually do anything, unless congress specifically passed a law saying a certain work has or does not have copyright protections, and which specific protections.
no more major questions doctrine