Already lobbyists try to run "education programs" with representatives as a means of influencing them (which works rather well). That tactic would be a lot more effective if representatives were perpetually lacking in knowledge about relevant issues.

And I'll bet a lot of these randomly selected representatives will choose to be educated by the group that takes them to a fancy dinner and ball game after, or has donated money to their church rather than the one operated by the local chapter of a perpetually underfunded Walmart Union who offer stale cookies.

All of these things can be mitigated with stricter antilobbying laws, but then again, so can our current problems.

I don't see the problem as necessarily being worse with randomly selected representatives, and in some aspects it may work better (randomly selected hippies will tell big corps to take a hike) , but I don't see it as solving the problem structurally.