People already got angry about receiving Amber Alerts for children on the opposite side of the city. And there were all kinds of technical issues -- sometimes even people's phones crashing -- when they were first testing this capability.

Adding erroneous nuclear alerts into the experience isn't going to make people feel very secure about the service or their neighbourhoods. People will just change their alert sound to silence, or something that won't wake them up even in the case of a real emergency (that boy who cried wolf you mention). Then it expensively helps no one.