Yes, parents are busier than ever. They sometimes feel helpless against the onslaught of the entertainment and advertising industries. But no one forces us to buy Hollywood's carnage or the foul-spoken lyrics that pollute some CDs. No one forces parents to subscribe to cable networks that show gratuitously violent movies. If you read the FTC report, you'll discover that parents overwhelmingly say they like the rating systems that alert them to material that's inappropriate for their kids.
Ratings have their own flaws, but they're useful.
There are several legitimate remedies for speech we loathe. One is better speech. They may be amoral, but they do care how people spend money. A noble purpose of the First Amendment is to guard people's right to say what's unpopular, even abhorrent. You may feel sick to your stomach today when you protect the speech you loathe.