I think you're generalising a little bit too much. Of course it is very common in politics that the "power hunger" kinda shines through every now and then and it often seems that the only reason we have politicians is that they could be at each others throats and gloat who's better and richer and so on. But I believe or at least want to believe that in the end of the day there are a lot of politicians who really fight for their country's and people's well being, but maybe they don't always get noticed as much as these havoc wreckers.
Also, how would you see a country work without leaders? Without anyone who could actually be responsible for the decisions made? In a way anarchy seems cool and all "living without rules" yet wouldn't that conclude with "the purge" kind of a situation. As you stated "what can we do to change that other than killing them" also shows that this sort of an approach where everyone can just do whatever they want if they do not like something wouldn't be very sustainable.
What we can do (other than killing politicians

) is that we too can work towards our beliefs and do what is in our hands to make our country and its' people lives better. And even if we don't have the power to control the political situation we do have the power to make people surrounding us feel better and therefore make their lives better a little better do.
I think that instead of letting politicians do whatever they want once they reach power over a nation, we can actually stop voting for the same liars.. Or, if people get out on the streets would have a real voice and the power to say something, a world with no corruption or "bad politicians" can actually be achieved. Unfortunately people have become chickens in time and they think more about: "i want to live tomorrow as well" instead of doing something even that might cost their life in order for their children to have a better future.