I don't see anything necessarily wrong with having bows and arrows - just make them futuristic like nearly every game set in the future (Crysis 3, BO3, Destiny, etc.) is doing. It's like saying that the game shouldn't have guns because the concept existed far back in the 1500s-1600s and is too 'old' for a game set a thousand years later. If you can make guns fit in the future, then you can do the same here.
Since the game is set in the future, bows would almost be on par with guns because battlesuits would most likely provide the person wearing it with augmented strength and capabilities to be able to efficiently hit targets with both speed and power, as opposed to today, which requires sole human strength - a variable that differs from person to person. The point of science-fiction is to use your imagination to make things fit where they are.
assasinguy wrote:Whilst I do love the recurve bows in Far Cry 3, (which is where you seem to be getting your inspiration for this), I agree with the others, a crossbow is more fitting for this game.
He mentioned in the OP that the idea was inspired by Crysis 3, which has a bow in the game and is also set in the future (2050-2060s).