Isn’t the President able to appoint people to do these things? It’s not clear to me this is not permitted.
According to Just Security, Trump can drastically curtail USAID with executive actions alone; however, he “may not unilaterally override” a statute by executive order. USAID was established by statute as its own agency via Congress in 1998 after first being created by executive order in 1961 by President John F. Kennedy. Since an act of Congress established it as an independent agency, an act of Congress would be necessary to dissolve it. - Forbes
Could the USAID agency could continue to exist, on paper, with a single staff member?
And he didn't even appoint Musk. Musk isn't head of any government department. He's just a random guy who has a ton of money.