Imagine Google or Facebook hiring 5% of their developers by lottery. Take all applicants, no questions asked, pick randomly.
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.
I imagine in that scenario that Google and Facebook would get particularly good at resilience and security.
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.
Consider that the system would be rethought accordingly, though.
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.
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.