Early firearms had projectile velocities somewhere in the region of the speed of sound. I suggest that it is unlikely anyone would see the trajectory of the ball. The next most obvious thing to check is, does this model give correct-ish predictions of where the ball lands? And then I'd have to say, it's not obvious to me that the prediction would be wrong. There's such a thing as air resistance. It might well be correct to within 10% for the part of parameter space they cared about, namely firing at castle walls at less than a mile, noting that gunpowder varied, windage varied, and the position of the gun after being hauled back into battery varied. Observe that siege guns weighed multiple tons and were shifted by muscle power, human and oxen. Exactness of positioning was not in the cards.

Given all the other variables, a rule-of-thumb approach didn't have to give you a whole lot of accuracy to be good enough. I observe also that you don't want to hit a wall with your projectile going straight down; you want to hit it in the flattish part of the trajectory, preferably low on the wall. So what happened at the end of the trajectory might not be that interesting to an actual gunner, it might be there mainly for decoration, like dragons at the edges of maps. Perhaps all they needed to know was that the trajectory was reasonably flat for X yards, and then outside of that range - well, don't set up your gun that far out, you'll waste your ammunition. Don't you know that gunpowder is expensive?

As for streams of urine, come now. You don't have to accept Greek elements to think that a stream of liquid does not behave like a discrete hard object, especially when the initial speed is so different. The kinematics are the same but the aerodynamics are not. And who pisses at an initial upwards angle, anyway?

Finally, let me point out that Galileo's great invention for studying trajectories was not any sort of mathematics, but an inclined plane that slowed things down so he could observe them with the naked eye. This suggests to me that nobody here was going to do any better in trying to look at cannonballs going half the speed of sound, or for that matter streams of urine.

While this model is closer to reality than the original prediction, I still cannot help but think... How could they deviate from observations so strongly?

The trajectory where the object ends falling in a straight line is the observed trajectory for many objects, because air resistance slows them until forward motion is imperceptible. Cannonballs probably flew too quickly to be easily observed. The only person who knew that a cannonball was about to be fired and thus would be ready to watch it, would be standing at the cannon, and thus unable to perceive its trajectory in any case.

I agree, though, that if people played catch with balls, somebody watching from the side should have noticed that the ball never fell straight down at the end.

Air resistance?