I should add that the American judiciary system is a functioning meritocratic system, any not only in large part non-democratic but where it IS democratic many people believe it should be.
In fat, the vast bulk of the American government is non-democratic and, provisionally, meritocratic - though often it is simply bureaucratic and crony-tastic.
The entire point of the american executive branch having only such a limited number of elected members is that their primary duty is often to uphold the principles of meritocratic assignment as best they can - there's a reason why there's a long idealistic traditional myth of appointing opposition figures to important government positions within the US, simply because they are the best man (or woman) for the job. Mind you, this, like the filibuster, is probably less true in reality than people might imagine, but the image people have for what the role of president is for is often pretty clear here. This is why the President can appoint people but the congress is supposed to "confirm" that they are in fact the best for the job.
There is a reason for the whole "Electoral College" thing - the executive branch was always supposed to be more meritocratic than democratic, with democratic influence but "controls" in place to insure that wasn't the only consideration.
I think there are better ways to handle this than the current American system - I think we could do quite a bit to make our meritocratic government elements more pronounced and more effective (and less culpable to cronyism and other such problems) by scaling back a number of democratic elements.
I think that ultimately any superior system WILL require democratic elements, just like any effective government requires meritocratic and bureaucratic elements, but I think that often times less democracy can result in a better government. Democracy serves a number of incredibly useful functions for a government, but any effective government is going to be a "mixed system", if you will, and I think our current democracy-dominated systems might not be as effective as a well-tailored system with less democracy.