Assassination, torture, and infringement of personal liberties are seen as horrible things and even a slight against democracy in modern western civilization.
Respect for Human Rights is a part of the Zeitgeist of most nations in the whole world, thus, Rowling, a member of one of these nations, has imputed the negative weight of these taboos in the Magical World to the three Unforgivable Curses: Avada Kedrava, which kills an individual; Crucius, which tortures an individual; and last but not least Imperius, a curse that prevents individuals to enact their free will.
You could also take it from a moral perspective, to do this, let's take a quick look at what each of the Unforgivable Curses does:
Kills the individual to which the curse was aimed at.
It causes extreme pain to the individual to which the curse was aimed at.
It allows the caster to control all of the actions of the individual to which the curse was aimed at.
Modern "western" society
Since the French Revolution, with its famous motto Liberté, égalité, fraternité, the western values suffered a turn on its social structure and hierarchy, with the given time, the western nations were moving from their very powered-centered society to a more democratic and republican approach.
This will lead to nations where the "voice" of their population is heard and have weight on determining the permanence of the people in positions of power. Humanity sees, for the first time in modern history, an elite that needs to seek legitimation from the general population.
We advance a few centuries in time and we have multiple democratic (some are quasi-democratic and others are straight autocratic states) and powerful nations coming to a clash in WWII. This war has the biggest loss in human terms from the entire human history and is the source of many of the most horrendous cruelties that the modern world has seen.
So, in 1945 the UN is created and in 1948 the world witnessed the creation of the Universal Declaration of Human Rights. The UN founding and the Human Rights Declaration are a direct answer to this war's barbarities. In the Declaration you can find the following articles (highlightings are mine):
Article 1 - All human beings are born free and equal in dignity and rights. They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.
Article 3 - Everyone has the right to life, liberty and security of person.
Article 5 - No one shall be subjected to torture or to cruel, inhuman or degrading treatment or punishment.
The morals behind these articles - even though most people don't know that they exist as articles 1, 3 and 5 of the Human Rights Declaration - are an inherent part of what western civilization considers as good.
Killing, torturing, and unfairly depriving people of their liberties are no longer tolerated by the republican societies that comprise a considerable part of the western civilization.
As history went on, the population started to become more aware of their needs, rights, and duties, thus as a society, throughout history, we were conditioned to think that our rights should be defended at all costs, and any attack against our rights (here exemplified by the right of life, of well being and of freedom) are seen as inherently bad.
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.