Well welcome to the absurd real world. That's the way it is.
You should read the authentic Framers and not derivative treatises.
The U.S. Constitution:
Article IINote the general relation between the branches is laid out therein, and what you are calling a weak presidency is nothing of the sort, after all, he can adjourn one or more of the houses of Congress. BUT, he must enforce only what laws the Congress issues. Not his own "policies."
Section. 2.The President shall be Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States; he may require the Opinion, in writing, of the principal Officer in each of the executive Departments, upon any Subject relating to the Duties of their respective Offices, and he shall have Power to grant Reprieves and Pardons for Offences against the United States, except in Cases of Impeachment.
He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur; and he shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law: but the Congress may by Law vest the Appointment of such inferior Officers, as they think proper, in the President alone, in the Courts of Law, or in the Heads of Departments.
The President shall have Power to fill up all Vacancies that may happen during the Recess of the Senate, by granting Commissions which shall expire at the End of their next Session.
Section. 3.
He shall from time to time give to the Congress Information of the State of the Union, and recommend to their Consideration such Measures as he shall judge necessary and expedient; he may, on extraordinary Occasions, convene both Houses, or either of them, and in Case of Disagreement between them, with Respect to the Time of Adjournment, he may adjourn them to such Time as he shall think proper; he shall receive Ambassadors and other public Ministers; he shall take Care that the Laws be faithfully executed, and shall Commission all the Officers of the United States.
Section. 4.
The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.
He can only recommend such to them. I.e.,
...recommend to their Consideration such Measures as he shall judge necessary and expedientHe can't arbitrarily simply begin doing things in controvention of law, and attempt to subvert the Constitutional design. The President might issue a bunch of tough Executive Orders, and secret ones at that, but they better have some grounding in existing policy authority of law. And foreign policy is also circumscribed. The notion of Agreements bypassing the Treaty-making requirement of Senate concurrence was never imagined. And he is ultimately answerable to Congress if he fails to keep to his oathe of office. If he gets too big for his britches, or manifests treasonous betrayal of the Constitution and country, as did Clinton, Impeachment is the ultimate retort available.
I have a Federal District Court ruling sitting on my desk (that I haven't read yet, because it is long) that rejected your argument. And the U.S. Supreme Court rejected even hearing it.