I agree but only to the point that an independent agency setup by Congress exercises powers granted Congress by the Constitution and does not conflict with powers explicitly granted to other branches.

(And it's pretty unclear to me how the NSF, which is ultimately a method for Congress to spend money, could relate to any Executive powers)

Yeah that's the thing, what powers are even granted directly to the executive by the text? It seems to me that the whole unitary executive theory is based on the clause "The executive Power shall be vested in a President", where "the executive power" is never well defined.

The President commands the military, negotiates treaties, nominates various officials for confirmation. Probably the most leeway relates to being called to ensure laws are faithfully executed.

So it seems reasonable the Executive can police independent agencies to ensure they operate as authorized by law, but I don't see how that challenges the establishment or existence of lawful independent agencies.

NSF is one thing but say an independent agency that does things like negotiate treaties or command the military or nominate Supreme Court justices should be off the table

(But on the other hand, theoretically the Executive should be able to voluntarily authorize legislation that enables those things if they wanted to. Just saying I can see cooperation possible but a veto override probably won't work to force it on an unwilling Executive).

I meant my question to be a rhetorical question, but that was totally unclear in what I wrote. What I meant was to imply "the executive isn't even granted very many powers directly in the text".

I agree with you about the powers you enumerated.