You're talking about democracy in it's purest, most idealistic form, which nobody ever claimed existed. Arguing that X doesn't exist because it's most pure, idealistic interpretation doesn't exist is nothing but pretentious navel gazing. It's essentially the same argument that communists use to say communism has never been tried.

Yes, democracy exists, in many forms and in many interpretations. Just because none of them achieve the ideal doesn't mean democracy doesn't exist.