The thing about killing princes and elites is that if you really think about it, there are only a handful of "elite" people compared to the number of people that have to follow them in order for them to have power. If you just keep killing them, you'll run out of them eventually, and the people under them now have a good reason to fear you and to follow you instead of their now dead former leaders.
This is not a new concept, which is why history is filled with political assassinations, coup de'tats, civil wars, and other power struggles. Of course the people in charge would want you to think it's impossible to win. It's because they're afraid that it is possible, and that you could just wipe them out (seeing as they're small in number) and just take over yourself.