In Harry Potter and the Deathly Hallows, Voldemort and his Death Eaters used the Taboo curse with Voldemort's name, making the word "Voldemort" taboo. Whenever someone speaks a word that is taboo, the caster is alerted of the speaker's location. In that way, Death Eaters several times immediately found whoever said Voldemort's name.
So why doesn't the Ministry of Magic use the Taboo curse on the Unforgivable Curses (Killing Curse - Avada Kedavra, Cruciatus curse - Crucio, and Imperius curse - Imperio)? In that way, they can immediately know if someone used an Unforgivable Curse, find them, and arrest them at once.