"Independent agencies don’t exist" is not a serious description of how U.S. statutes and doctrine work. "Independent agency" is not a vibes-based label. It's standard terminology for agencies Congress structures to be somewhat insulated from direct presidential control (e.g. multi-member commissions with fixed terms and (often) for-cause removal). Congress has, in fact, established a number of such agencies headed by multi-member bodies whose officers may only be removed by the President "for cause." [1]
The Constitution may not use the modern civics phrase "executive branch," but it plainly creates what we now call one: "The executive Power shall be vested in a President..." Even if we grant the semantic point, it doesn't prove the legal conclusion you want. Congress's authority to create agencies and offices and design their basic structures (subject to constitutional limits) is well-recognized. [2]
You're also wrong to treat Myers v. United States as if it ended the discussion. Myers involved a purely executive officer (a postmaster) and is part of a broader removal-power line of cases. [3] Humphrey’s Executor (1935) limited the sweep of Myers in the context of independent commissions by upholding Congress's ability to restrict removal of FTC commissioners to specified causes (e.g. "inefficiency, neglect of duty, or malfeasance in office"). [4]
Your analogy to "congressional aides" and "judicial law clerks" is a category error. Aides/clerks are staff whose authority flows through, and is controlled by, constitutional officers. Independent commissions are Congress-created offices exercising delegated statutory authority, and the question is how far Congress may structure that delegation (appointments, terms, partisan-balance requirements, and sometimes removal limits) consistent with separation of powers.
Finally, the Woodrow Wilson citation is doing sleight of hand. The passage you quote is about insulating administration from day-to-day politics ("administrative questions are not political questions") and it indeed contains elitist/racist language about voters. [5] But (1) that’s an argument about civil service/administration, not a dispositive argument about the constitutionality of independent commissions, and (2) it's historically confused to imply this is a late/progressive "invention": as early as 1887 Congress created the ICC with explicit bipartisan-balance language and explicit for-cause removal language. [6]
If you think Humphrey’s Executor was wrongly decided and should be overruled, that's an argument you can make. But pretending "independent agencies don't exist" (or that Myers settled everything) just isn't accurate as a description of U.S. law, and someone with your background and experience should know this.
[1] https://constitution.congress.gov/browse/essay/artII-S2-C2-3... [2] https://www.congress.gov/crs-product/R45442 [3] https://www.oyez.org/cases/1900-1940/272us52 [4] https://www.oyez.org/cases/1900-1940/295us602 [5] https://teachingamericanhistory.org/document/the-study-of-ad... [6] https://www.archives.gov/milestone-documents/interstate-comm...