What if they abuse that trust? If they delete your entire hard drive when their software recognises an illicit key (regardless of phoning home - software can have an embedded list of known pirated keys), what are you going to do about it? You trust them to leave your computer unharmed when they find you using an illicit key. Morally: The software authors trust you to buy their software legally you abuse that trust. This might be funny (for example, the game Crysis gives pirates a gun that shoots chickens instead of bullets) or it might be serious, like deleting all your personal files. Technically: Some authors have even put in attack code that runs if you use their software with a well-known pirated product key.
They may not go after you if you're a poor individual, but they love taking businesses to court, even if it bankrupts a small business. Software commonly 'phones home', even in the form of checking for new updates. Legally: If the authors of the software find you are using illicit copies of their software, they are at liberty to file a civil copyright infringement claim against you.