A man may see how this world goes with no eyes. Look with thine ears: see how yond justice rails upon yond simple thief. Hark, in thine ear: change places; and, handy-dandy, which is the justice, which is the thief?
King Lear is not disgusted with the world because of being betrayed by his two daughters but rather because he had never really seen the real world before his quarrel with Goneril and Regan impelled him to go out into it. His disgust is largely based on what he has seen and personally experienced since that event precipitated it. His daughters were only examples of humanity. There were many more to follow.
Lear's disillusionment with the world can be compared to characters like the Prince in Mark Twain's The Prince and the Pauper. Lear can also be compared with Cervantes's Don Quixote, Mark Twain's Huckleberry Finn, Charles Dickens' Oliver Twist, and J. D. Salinger's Holden Caulfield. There are many other such characters in literature, including Pip in Dickens's Great Expectations, Herman Hesse's Siddhartha, and the hero of Voltaire's Candide, who starts out thinking that everything is for the best in this best of all possible worlds.
Lear led a privileged and sheltered life. He had a false impression of humanity because he was surrounded by flatterers. When he decided to "abjure all roofs," he had no idea what he was getting himself into, although his Fool certainly knew from a lifetime of abuse what to expect from most people in the world at large.