Only to those who hyper-analyze the "dies, resigns, or is otherwise unable" language in the statute. If what you say represents some point of real life contention (can;t use Vacancies Act when the position is vacant due to being fired), why isn't there a "Vacancies Act uproar" over replacing Tillerson with Pompeo?
-- Also, the appointment under the VRA can only last for 210 days, and the person so appointed is not eligible to be appointed to permanent Department head. --
That's on the Senate. The "210 day" value isn't "straight up." 5 USC 3346 anticipates contention versus Senate confirmation, and can start the 210 day clock when the Senate rejects a nomination.
-- and the person so appointed is not eligible to be appointed to permanent Department head. --
I believe that is false, but I'm open to citation of history, or statute, etc. If what you say is true, Pompeo's nomination to Secretary of State will be void right off the bat.
Pompeo is not appointed under the VRA, he’s nominated to the post as per usual procedure and is subject to Senate consent.