Calls to crack down on offensive speech in the US have come from almost all sides of the political spectrum. Of course, there are pros and cons on both sides of the argument, but the law has erred on the side of protecting the freedom of expression.
Freedom of expression does a lot of good things for people. For example, it gives people the power and comfort they need to express themselves without fear of government persecution. It also, importantly, allows people to criticize the government and its various secondary parts, which holds true to the Constitution's original goal of making the government operate according to the people's needs. Freedom of expression can also expose corruption or unlawful activities; many times, scandals in major corporations or even the government have hit the news because a journalist or investigator wrote about it. It also allows people to challenge those who do have offensive or hateful views, defeating them with their own ideas.
There are also, however, cons to freedom of expression. First, it can spread false information, especially on the internet. We see this severely in the anti-vaccination movement. There have been numerous medical studies indicating that vaccines do not cause autism in young children, yet thousands of children in America went unvaccinated last year, causing measles outbreaks. Even expression that is offensive or mean is also protected, which means it can incite violence against others.
Generally, though, the Supreme Court has sided with protecting freedom of expression. Once we start filtering what constitutes "good" and "bad" expression, we expose ourselves to abuse by the government and other major powers in the US. These are powers that have far more money and resources than the people do and can put down speech they don't like. The free exchange of different expressions and ideas is key to a democracy.