Not all. Weapons like The Last Word/No Land Beyond/Universal Remote feel plenty exotic without a burn. These are also the ones that are mainly crucible weapons though, one more reason they don't really need the burn. On the other hand most other primary exotics I would agree could definitely do with an elemental upgrade.
Right? Don't get me wrong, when primary damage is favoured, the No Land can wreck (Bonus damage to the highest single round damage on a primary). But it's situational and you better know how to use it really well.
Overall though theses weapons are seemingly intended for crucible only. I mean, The Chaperone has a quest to get kills in the crucible with THE LAST WORD. If that doesn't make it clear to people I don't know what will. Even the lore supports this. All the grimoire cards talk about gunfights between guardians/outlaws, not fighting the alien incursion.
Sorry, long response.