Don't misinterpret my recent posts on the idea of the U.S. adopting a shadow cabinet system. I'm not advocating that.
I'm skeptical of any proposal to mix and match elements of a parliamentary system and a U.S.-style presidential system. That can lead to unintended consequences, as was the case when Israel tried to graft the concept of direct election of the head of government onto their parliamentary structure, as I wrote about in this post.
Also, some C-SPAN viewers, after watching Prime Minister's Questions from the British House of Commons, want our president to face similar questioning in Congress. But I don't think that fits with our separation-of-powers concept. The American president is not a part of, and answerable to, the legislative branch, in the way the British prime minister is.
Additionally, I think it would be difficult to introduce some or all of the aspects of a parliamentary system in a country such as ours, whose political system did not evolve that way. American political culture evolved around the elements of our constitutional structure. A similar process happened in Britain, over the centuries during which their parliamentary system developed.
There has been some convergence. For instance, some U.K. commentators lament the degree to which the office of prime minister has taken on presidential trappings. Their view is that the prime minister has gone from being first-among-equals in the Cabinet, to governing from 10 Downing Street with his or her equivalent of the White House staff.
But to decide that, as of such-and-such a date, either one of us would suddenly change over to the other country's way of doing things, as Sweden did when it changed from driving on the left to driving on the right on September 3, 1967, would probably be chaotic with who knows what consequences.