Except for one chapter on epistocracy, the book addresses an army of straw men. These straw men are placed to teach informal political theory at elite universities. They preach democracy, but apparently not because democracy leads to better outcomes than alternative arrangements. By contrast, the book maintains that democracy is only as good as the outcomes it generates. Duh!
Brennan argues that, perhaps, epistocracy should be given a chance. Perhaps. To some extent, we already have a version of epistocracy. Voters do not directly decide on most policies. (When they do---for instance, in referenda---they often err badly.) The sophisticated individuals lobby, advertise, lie, and argue, thereby hijacking the votes of the less sophisticated.
Successful democracies are delicate systems. No one understands why they succeed, although many can provide a plausible rationalisation for why they might. Brennan has the right instinct: progress not by revolution, but by incremental intelligent design, trial and error.