And Gamebryo can handle crossbow animations (seriously, stop blaming absolutely everything on Gamebryo. It's a shitty engine, but why, oh, why wouldn't it be able to handle a specific set of animations?).
Really? Reloading a crossbow is more complex than inserting and removing a clip (and even, doing just that is no proper reloading method, but it's sped up for gameplay purposes I wager). You need to stand still. You need to pull back the string, hold it, put the new bolt in, and carefully adjust the whole thing so that it's ready to fire. Even for a profesionnal, it takes some time, and anything else would be arcadish on screen. Look at the reloading on Gamebryo; half of the reloading animations look pretty choppy to me, as well as being incomplete (not accounting for the bullet in chamber? No safety? ect.). A crossbow is very hard to properly animate, the character needs to stand still for it not to look silly a hell, you have to account for the string, the proper position of the bolt, movement must be fluid.
That said, you could have an automatic crossbow (like Bioshock's), but the bolts on these are smaller and have difficulty penetrating anything but very light armor (not that it stopped said Bioshock crossbow from 1-shotting hulking monstrosities in armor that can survive crush depth, but hey, it's a game where genes make you shoot lighting). Not very useful in a wasteland. And what's the point of having a crossbow if it more or less functions like a weaker gun anyway?
Finally, I checked a bit (OK, Wikipedia, but don't hit me!) and forces using crossbows today don't use them for combat; it's for things like establishing zip lines, triggering booby traps and tripwires at range, or to stop people carrying explosives to prevent detonation. All are very, very niche uses. In almost every situation a crossbow is useful, a gun is better.
That said, I do agree Fallout has no shortage of weird weapons (acidic water launcher and makeshift gravity gun anyone?). A crossbow would not be out of place as an unique weapon of sorts, but I wager it's just too hard to make such a complex animation for one weapon.