Your second example is what I actually would like to see in the game! It is really a major detail for understanding lore and story, while investigating every corpse I think can get rather tedious.
No no. My suggestion isn't to investigate every body. More like as you approach the Dead goblins near Gale, a single Investigation check is made for each character. If one succeeds, your Compendium is updated.
Same for the fisher people on the beach. As you pass by some, a roll is made. By others, another roll for some additional clue. Stuff like that.
