Even if guns are commonplace in Fallout, it's still GOT to be easier to find (or create) a sharp pointy stick or metal scrap rod to shoot with a bow than to find a proper calibre of ammunition to fit your gun (which you have to meticulously keep clean and oiled and so on)....
Granted, a face off between an archer and someone with a machinegun will go poorly, but the archer isn't ~designed~ for that kind of encounter. Just like you would be better off with a melee weapon or shotgun while clearing a building with narrow, twisting hallways, instead of using hand grenades.... the grenades do more damage, sure, but in a close area you don't want to be dropping them at your feet. Different weapons for different goals.
In the Fallout universe you could even get relatively whacky with it, having "tranquilizer" arrows or "taser" arrows (miniature power supply fuels the zap).... and of course explosive-tipped arrows...
Unfortunately, as someone noted above, the game mechanics may make it difficult to seamlessly integrate a new ~type~ of weapon like bows/crossbows, etc. But then, that's where modders can step in.
Heck, for that matter, I would not be surprised if modders could create their own perks (Archer, Fletcher, TrickShot, etc) as well as the actual weapons (and animations).