The United States is a democratic constitutional republic. As such it is subject to all the functional problems of most conventional representative democracies: Manipulation by special interests and a division between professional policymakers (politicians and lobbyists) vs. a largely passive, uninvolved and often uninformed electorate. There is also the cost of elections! The last US election (2012) cost was $6,285,557,223! Over six billion dollars!!!
Now would not a random selection of policymakers make it easier for everyday citizens to meaningfully participate, and harder for special interests to corrupt the democratic process? A random selection of policymakers from the adult population, based on certain and specific and qualitative criteria like citizenship, age, education and mental health, would certainly contribute to a more representative and better government than the current system! The ancient Athenian democracy, for example, made much use of sortition, with nearly all government offices filled by lottery rather than elections!
Certainly, under Lottocracy, also the cost of politics would be far less!