First off real thanks for elementary school physics, I passed it with flying colors as it happens.
It is not my intention to measure everything with a milimeter tape, especially considering how abstract the model is - no matter what gun freaks would want.
Obviously I didn't mean crossbow have flat trajectories - I was talking about their tactical role. Naturally every projectile follows a ballistic path. And obviously the engine doesn't allow to tweak it - you can either shoot artillery-like, or completely laser-flat. The latter was chosen for crossbows because of the aforementioned tactical role. Crossbows lacked sights for long-range sniping, and they were intended for use with non-elite personnel - they were usually used at ranges of up to about 30-40 metres. You can study the medieval art of fortification to learn more (towers spaced within crossbow's effective range, etc). In Piratez, it's obviously not really to scale; crossbow's limited utility at long range is represented by sharp long range acc penalties.
Having said that, bows top off at 80-ish lbs, while a crossbow can have 150, 200 or more - which naturally makes the trajectory more flat. But that's wholly beside the point. If we took the Asian aproach, then, indeed, a crossbow would fill the same tactical role as the bow and would follow a ballistic path - but where would be variety in that?