I can't fathom why people think "managing a country" requires less skills than managing servers. The consequences of hiring someone unqualified is certainly not less severe.
Once you've got enough people, 5% of them may as well have been hired by lottery, depending on what you're measuring. People get less productive, more productive, want to change the company, decide to steal things, etc.
I think it's interesting to think about.
Representatives picked by lottery would not "manage" the country: they would hire qualified people to do so, and they would supervise their work according to their values. The point of the lottery, at least the way I see it, is to have an unbiased random sample of the population oversee the government, but not to actually run it.