It isn’t designed that way. The Constitution sets up a system of separate institutions sharing powers, and there’s just no way around that. The Constitution sets up two separate, independent, coequal chambers of Congress, and there’s no getting around that, either. The Constitution sets up 100 equal members of the Senate and 435 members of the House, and no one can tell them what to do, either. And, no, no chief justice can tell the associate justices how to vote — and certainly no one from the other branches can tell the supremes what do to.
More than that: Because executive branch agencies and departments are, by design, responsive to both Congress and the president (and the courts and, in practice, to state governments and private interest groups and the parties and, most definitely, to their own bureaucratic preferences), no one can order them around either.
Sure, sometimes politicians play the game so well they obtain somewhat more influence than their position alone would grant them, but those gains are almost always very modest — often enhanced by illusions of “control” fostered by canny politicians themselves (including those who are doing what they want but crediting it to a president or a speaker) or invented by reporters eager to crown “winners” and “losers.” Sometimes elections give like-minded people so many offices that it’s easy for them to coordinate their actions, but that’s not about anyone in particular in control; it’s just that a party temporarily has the votes for their highest priorities. And even then, most of it, again, is illusion; look closely at the agencies or the Hill subcommittee rooms, and you’ll notice hundreds of independent actors who are mostly ignoring whoever is supposed to be running things.
No, no one “runs” Washington. The last — perhaps the only — time anyone came close would have been Franklin Roosevelt in his first several months in office, but even that is probably overstated, and it didn’t last long. During normal times, no one comes even remotely close to “really running” Washington. It just doesn’t work that way.