Suppose we pick elected officials at random. OK, in the first round we get a bunch of reasonable people and they do a bunch of reasonable stuff. In the second round, maybe the same thing, except that they have different ideas from their predecessors so they end up repealing all the programs and replacing them with still reasonable but quite different ones. Businesses can't plan anything because they don't know what the regulatory environment will look like the year after the election. The churn strains our already-difficult ties with countries like China, Russia and Saudi Arabia when the things the Nth Congress promised get repudiated by the N+1th Congress which is comprised of entirely different people.
Then, sooner or later, random chance produces a majority coalition consisting of people who are willing to horse trade for corrupt programs that specifically benefit their own friends and family, or "libertarians" and peace activists who very suddenly disband the entire U.S. military, or nationalist religious fundamentalists who decide to declare war on "Muslims" or drop a nuclear bomb on somebody with the ability to strike back.
The thing about politics is that you actually do want professionals running the country. You want people with formal training who know what they're doing. You just have to make sure they're representing us and not somebody else.