To put it another way: when one person shouts over the media mess and
claims to speak for all of us, it kinda matters what that one person is
saying. And suing someone for childish racial ridicule can invite, well, racial ridicule for childishness. Lawsuits do not always encourage discourse. Highly publicized lawsuits, like this one, often serve as a tit-for-tat "take that" slap in the face that do little to explore our underlying prejudices and current racial climate. And they're not well-designed to promote a wrongdoer's understanding of the wrong. (Cyrus' second apology wasn't so hot either.)
Not to say that all tolerance-based lawsuits are frivolous. Legal and investigative action is often necessary when it comes to racial discrimination in the workplace, or bias against same-sex marriage, or other cases that broadly affect a community, like admissions quota caps for Asian Americans in the University of California system in the 1980s. Some situations need that extra shout in legalese to be understood as civil rights causes. Miley Cyrus and her "goofy face," while annoying, do not constitute a civil rights cause that calls for a lawsuit. It's just bait for FOX News.
That said, I think the little song Margaret Cho penned on her blog is much more effective (and zing!-worthy) than filing a lawsuit. Sending a letter, like Alvin did, is a helluva lot more effective too.