What we actually have is representative democracy, where the choice is often nominal, and leaders generally come from the same class in practice (and represent the interests of that class). So the fact that people don't "vote them out" is not an indication that they don't care enough - they might care but not have the choice that would reflect it.
It is also susceptible to "don't let the other guy win!" type of propaganda, especially in FPTP electoral systems like the American one. So long as you can find enough emotional wedge issues to ensure that your base will never even contemplate voting for "the other", you can basically do whatever the hell you want.
They can't do whatever they want. They can do more than you'd want them to be able to do, but they can't just take billions of dollars and put them in their own pockets. Company bribes makes every American politician a multi millionaire, sure, but if they could do what they wanted they would be multi billionaires like the rulers of Russia and China.
Which is why we have a democracy so that rulers don't have to worry about getting killed in a rebellion and people can choose a new ruler when corruption gets bad enough.
This of course means that corruption tends towards the highest people can tolerate. So if you see corrupt politicians it is because people tolerate it, if they wanted they could vote them out but people as a group don't care enough to actually do the work necessary to do so. However if corruption grew large enough as you fear then people would start caring and things would change rather quickly.