There is little evidence that Mill advocated an unhampered marketplace of ideas. In fact, there is evidence to the contrary—that he preferred a kind of “affirmative action for unconventional opinions.”
Today's conflicts revolve around the desire to grab hold of someone else's property using the tool of compulsion that is the state. Would we be more peaceful and prosperous if it followed the liberal program? The question answers itself.
Liberalism was the most popular and influential ideology during the nineteenth and early twentieth century. So, every new socialist and authoritarian movement defined itself as "liberal" to capitalize on liberalism's popularity and importance.