Theoretically, by wiping out the rich would create instability within the wealthy class, they wouldn't have the time or the means to herd the politicians to serve them or to effectively disrupt democracy.

The inheritance that kid collects would amounts to "Congratulation, you won the lottery, now what? You haven't own any corporation yet, know of anything about how to make connections with other politicians and wealthy class of people and so forth. You're pretty much on your own."

Like 70% of the time, those people wouldn't even bother with politic and would just spend the money vacationing where-ever in the world and having fun with the newfound wealth, not busy trying to disrupt democracy. People tend to be very shortsighted when they amasses huge wealth, in fact, according to some statistic, it ranges from 44% to 70% of people who gain huge amount of money end up losing it all within the next 5 years.

That amount of time would basically give the common people enough time to go about fixing the political system.