It's easy to call it dramatic, but it's important to remember that these are intended to grab our attention and inform people of potential hazards. They may sound dramatic, or they may sound scary, but if people end up paying attention and listening to what they need to do to stay safe, then it's worth it.
For example, take these alerts from Australia and Japan:
With the first clip, you could very well miss critical information if you weren't paying attention, if it wasn't for the siren. As for the second clip, whilst the Earthquake Early Warning might sound relatively tame, it is a sound which pretty much any Japanese person would recognise, and use it as a cue to drop, cover and hold.
It is good to remember with these videos that, whilst warnings may sound dramatic, they are like that for a reason.
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NYTV, WW Update and Quatorzine Neko gave kudos