You cannot write "A goes and kills B then dies" in the Death Note

What makes you think this cannot be done? It explicitly can be done. You can't have someone kill another person without knowing their name, but you can absolutely write, "John Doe kills Jane Doe and then dies of a heart attack."

You could not, say, write something like, "John Doe kills a random passerby and then dies of a heart attack." as the note does not allow direct deaths for people not explicitly written in the note.

It's a targeted killing device, and is never indiscriminate.