A death threat doesn't lack credibility because it's anonymous. It doesn't necessarily lack credibility even because it reads like an obvious dimwitted trolling attempt. Sure, the vast majority of such threats aren't serious -- but it only takes one that turns out to be real.

They don't need to be credible to ruin someone's life. If you talk to people this has happened to, they can't sleep, they end up moving, they stop leaving the house, etc etc. The perpetrators should be prosecuted as if they are all credible.