Crossbows seem to do slightly less than 1.5 times the damage of a normal bow at the same level, for 1.5 times the ap cost.
Even if it was a full 1.5 times damage, a crossbow would still be at a disadvantage compared to a longbow due to the fact that the 4 ap system is super granular. I definitely agree with you that a 3ap cost in a 4 ap system just can't really work. Being only able to attack once the first turn, then twice the second compared to twice each turn is much less reliable. Its hard to quantify exactly how much of a handicap that is, but it seems significant to me, at the very least.
I would guess the devs reduced crossbows damage proportionally because they thought it would be too powerful with some abilities. Like, a high finesse archer with a crossbow using marksman's fang might just outright kill some enemies without touching armor, or a stealthed archer with a crossbow might start a fight out with Sniper and get a kill right away. The crit chance on Hothead makes these things even more likely. I can't say for sure if that's their reasoning, but that's the only thing I can think of.
I think the biggest issue staves have is that there are no convenient gap closers in a magic skill class. Like, I don't want to have to take Warfare and get bonus damage to physical armor if I have a high intelligence, because the only way I could make use of that is Necromancy. And Necromancy is definitely not the class I build intelligence for. Its not bad, but I'd much rather be able to get environmental effects or crowd control on my Inquisitor. Anyway, you rarely get a staff that has anything but pure magic damage, so the armor bonus damage will be wasted on that at least.
Staves actually do a good bit more damage than a dual wand-wielding build, not even counting the damage penalty for dual-wielding; and the bonus to crit multiplier on the Two-handed skill is obviously more offensively oriented than the 1% bonus to dodge when leveling dual-wielding. If you could just get to the damn enemies while holding a stave without having to waste a point in a class that doesn't help you like Warfare, or having to take Bullhorns, which has terrible damage for a 2 ap cost, then a staff would be about as viable as a two handed sword, I think.
