I too felt like the game is missing a rather realistic aspect with this and actually ended up using a mod for that.
Death by Terror. https://www.patreon.com/posts/dbt-death-by-46554849
Fyi, I have no idea whether it works with the latest update for I myself have absolutely NO intentions to update for a while. I haven't had deaths by fright myself yet (even with a sim living in a haunted house) but you can always tweak the settings.