Treyarch has a crossbow and as much as I found it fun to use I felt that it just didn't give me enough satisfaction. I think a compound bow would be better suited for a FPS than a crossbow would. For attachments you could have varying arrow types such as standard arrows (have a fast RoF), incendiary (sets the immediate area on fire for a AOE), shock (immediately drains stamina and temporarily slows them), and an aluminum serrated arrow that's ( heavier and slower RoF but deals extra damage, OHK to head or chest).
The thing that really turned me off about the crossbow in Black Ops II was how slow it fired which really was self defeating considering how it didn't give you a OHK. With different type of arrow you're given the chance to still be productive with the weapon even if you don't get an immediate OHK.
The biggest advantage of using a bow is it's quiet, accurate, medium range, and deals a good bit of damage. It fits a unique category that has yet to be met by any weapon currently in the game. Sniper are slow handling and are inherently loud (minus the VKS). Shotguns don't have the best range or accuracy and they too are loud. A bow offers inherent traits that don't need attachments giving a player the ability to spend points in other areas.