I've found that you can absolutely chalk up "online death threats" to idiots vying for attention.

Impersonal (distant) threats are not created equal to in person threats.

Edit: The harm is subjective. The whole point of such a message is it's designed entirely to shock or offend. To give the pests actual power over you is the greatest part of the problem.

Not saying it should be ignored either. Instead of being melodramatic, we should be pragmatic like we were with email spam. The next step is to create tools giving greater power to the users to pro-actively prevent such nonsense.