@JTT,
I have no reason to assume that there have been regularly occurring examples of "stunning incompetence" appearing in the Presidency. In fact, i can think of precious few. Baby Bush was not incompetent, he simply pursued a program odious to a significant portion of the population, and pursued an economic program which a significant portion of the population considered discredited--to wit, "Reaganomics." Probably the least competent administration was that of Warren Harding.
But i did not say that that were a weakness, i was simply pointing out that the Westminster system does not necessarily choose a chief magistrate who might have been chosen had the office been open to a general election. Competence in the executive branch in the United States can be achieved, if it is achieved, by the appointment of the executive branch officers. This must be done with the advice and consent of the Senate. If the President does not actually advise with the Senate in his or her choices, he or she still must secure the approval of the Senate. Americans routinely demand democratic institutions, and that is a facet of democratic institutions.
By contrast, in the Westminster system, the leader is chosen by the party insiders, and he or she then chooses (subject to avoiding strong disapproval from party insiders) those who hold ministerial portfolios. If the party in question is not in power, than those same individuals become the "critics." He or she who would hold the foreign office portfolio were his or her party in power, would, when not in power, become the foreign policy critic. So long as he or she retains a seat in the Commons, if his or her party comes to power, he or she becomes the minister holding that portfolio. Therefore, Prime Ministers and cabinet ministers are subject only to the democratic choice of party insiders, and the electorate in the district in which they stand. The system is flexible enough (from the point of view of party insiders) that if someone is not returned from their district, they can continue to exercise the portfolio while awaiting a by-election in a "safe" seat. The origins of the system lie in the corrupt and elitist system which reigned before the 1830s and the first reform bill.
My comment did not claim that this were a weakness, but it certainly could not either be seen as a strength. Anyone who criticizes Reagan would hardly be in a position to praise Thatcher, who pursued virtually the same economic program. The competence of John Major and Tony "Poodle" Blair was as much a function of their choice of ministers and formulation of policy as is the case with American executive appointments.
My remarks were in response to a claim that the American system has obvious flaws. So does the Westminster system. Far more power resides in the hands of a Prime Minister than is the case with a President, and the Prime Minister also acts as the party leader and floor leader in the legislature, as well as being the chief magistrate, a flaw which our system avoids.
If these things are not obvious to you, or are not easy for you to follow or understand, that is certainly no fault of mine.