Rowling just took three of these essential rights and imputed the weight of harming them to three Unforgivable Curses in the Magic World of Harry Potter. For Rowling (and for most of Western society), these are the three most clear examples of attacks against human being integrity.
Even though you can kill people in the world of Harry Potter by other means as OP mentioned in his question, these three curses were tailored to directly go against these three basic rights that all human beings are entitled to have according to the values of most western (and non-western as well) societies.
Fiction is only one of the many mirrors that reflects the current condition and awareness of our society, so it's normal to see props such as curses, tech, charms, magic rings - and the examples go on and on - that, when approached from afar, will ultimately reflect our fears, insecurities, moral values, and many other aspects of the human society and nature.