A very good analogy. It is the exact thing that the liberals are suggesting doing to the 2nd Amendment.
The big difference is that the only one that would have any positive effect on reducing the violence would be an assault on 'Hollywood' 1st amendment rights to distribute filth.
I am not so sure that "filth" was ever intended to be protected by the first amendment. And neither were obscene or gratuitously violent images.
The first Amendment was instituted to mainly protect political and religious speech. It was not instituted to protect every kind of "artistic expression". But the protections of the first amendment when it comes to pornography and other soul destroying imagery has been expanded whereas the right to religious expression and the right to bear arms to protect yourself from monsters has been slowly but surely limited.
If Hollywood is going to lecture America on the Evils of guns, then we need to lecture Hollywood on the Evils of violent imagery and lay the blame for this tragedy at their feet.