Because others bear the risk everyone becomes safer.
Risk of terrorist reprisal is not butter, it does not get thinner as a you schmear it across multiple parties.
Let me use a model to explain this.
Say the Times creates and publishes a cartoon that provokes the terrorists. Johnny Jihad sits in his bunker, becomes irate, decides his cell will make a reprisal, and determines that his cell has a 40% chance of conducting a successful terrorist attack against the Times. So there's a 40% risk of a successful attack.
Now let's say the Post and the Daily News also pickup the cartoon and choose to publish it. Johnny's analysis of those two papers determines that his cell has 60 and 80% chances, respectively, to successfully attack those papers.
The chance of a successful terrorist attack now is 80% against one target, the Daily News. So the risk has increased.
However, it does not stop there. There are also 40 and 60% chances to attack the Times and the Post whose ratios of success are independent of the ratio of success to attack the Daily News. The choices by the Post and the Daily News to republish the cartoon do not reduce the risk to the Times, they merely create risks to themselves that are independent of the risk to the Times. The risk share does nothing to reduce the initial risk of the Times. It only creates risk for other parties. Ergo, the argument that republication in ten thousand other papers would create safety is baloney. It would only create additional instances of risk independent of the original one.
The even more crucial question however is what is the alternative? Give in to the terrorists' demands, to Islamic blasphemy laws, and self-restrict free speech?
There are two problems here. The first that you've suggested a false dichotomy, that the only alternative to your proposal is to give into the terrorists' demands. Which is utter bupkis because a third way of having ten thousand newspapers printing a diverse array of ideas is an alternative that does not give into the terrorists' demands.
The second is that ten thousands newspapers all printing the same thing isn't free speech. When speech becomes obligatory, it ceases to be free.