The key to draining the swamp is to have a President committed to draining the swamp. It is self-evident that Donald Trump was never that President. And he still isn't.
Not the only key, but the one most likely to be implemented. A thoroughly originalist SCOTUS could decide that Wicker v. Filburn was wrongly decided and that the Commerce Clause does not grant the Federal government the power to meddle in more or less everything on the plea that it "influences interstate commerce", thereby rendering the enabling statutes of a lot of Federal departments and programs, along with vast swathes of administrative law, unconstitutional
I will disagree with both of you - Though not fundamentally...
The president and his administration are always, as recently demonstrated, relatively temporary. A president still has to function within whatever environment he is within. And that greater environment is definitely liberal. He will come and go, and that culture will have changed very little.
With any luck, while the SCOTUS is certainly long in its term. its pronouncements are individually one-and-done. That can be very effective, but not as effective as Congress, where both the law and the purse reside... And secondarily, SCOTUS tends to be ancillary and insulated from the greater culture... It is its own thing.
The Congress is what that culture revolves around, like jackals around a carcass, attracted to all that money and power - There is no lobby for the president or the SCOTUS. There is for the Congress. and there is a reason for that.
In the end, not only does the Congress wield more power and control the money, because of that, it sets the tone of the culture. But it will take a real and sustained conversion to Conservatism to begin to impact the culture there, and therefore the swamp. A decade or more with real Conservative opposition if not control. As those Conservatives infiltrate that culture and populate it, inevitably it will become more Conservative - And operational Washington along with it.
Cutting off whole departments is grand - but in the end it is an attrition game.