I feel like the solution would be simple, though. Don't completely get rid of the calls. Even for acquaintances, it would be a nice touch to get a call. However, I don't feel that Sims should be getting such a long and powerful sad moodlet over the deaths of Sims who are only acquaintances, especially those that your Sims have only met once. Confirming what the OP said, the way this system works in its current state, all of my Sims are in a constant state of sadness. It really takes the fun out of the game. This is how I'd do it-
Death of Acquaintance: Fine moodlet for 6 hours. With this moodlet active, it'll take a bit of effort to get them into another emotional state, but at least they won't be sad.
Death of Friend: Sad moodlet for 12 hours.
Death of Good Friend: Sad moodlet for 24 hours.
Death of Best Friend/Boyfriend/Girlfriend/Spouse/Close Family Member: Sad moodlet for two days.
And another thing, toddlers shouldn't be getting these calls at all, plain and simple. They don't even have phones! How are they still getting these calls?!
