The dog that hasn't barked here is the Senate and the Senate confirmation process. Relying on a GOP Senate to exert some oversight over Trump is sort of laughable on the one hand. But remember, it doesn't take many. Two GOP senators defect and Mike Pence can break a tie in the administration's favor as President of the Senate. So at least three GOP senators would have to break ranks to block a nominee. But three is a pretty small number.
Given Trump's fixation on personal loyalty as close to the only criteria of service and given the sleaze attached to pretty much all the loyalists, what seems possible is that you get an extreme version of non-departmental government. In other words, confirmable people running the departments who have little sway with the president and real power controlled from within the White House where confirmation is not required.
To be fair, this is the trend of all recent administrations: concentration of real authority and power in the White House. But this could end up being an extreme version of that, and for driven by very different reasons.