No logical reason for a connection, or lack thereof, between accuracy and rate of fire. Unlike automatic rifles, where recoil throws off your next shot, it just takes a certain block of time to pull out an arrow, draw the bow and release. With a bow, you can't aim for longer than a second or two, because you are holding the bow at full draw.
There is, but not due the same reason. English is not my main language so maybe I'm not explaining myself properly.Rate of fire:
reloading a crossbow takes a while, you need to put it down to the floor (the heavy ones), put your foot on it and turn the lever with both hands until the "bolt container" is back to fire position. Then close the "lock" and put the bolt on it. A bow just requires to catch an arrow, pull it back and release.Aiming and accuracy:
in battles, archers usually didn't shoot directly to a man. They shot at the mass of men in a parabolic trajectory. Trained archers start to aim as they bring the bow to fire position. I mean, in the same movement they pull back the arrow, aim and reach fire position. So they can release the arrow after 1 or 2 seconds or even less if they do indirect fire.
A mid-trained shooter can get a decent accuracy with a crossbow for some reasons. It is shot like a rifle, easier than a bow; you don't have to keep the pull, so can take all the time you need without any effort; and you may have the aid from some primitive aiming device. That was the reason crossbows and after gunpowder weapons took over in the battlefields: you get a good fire power just equipping recruits with those weapons. They don't need a long time training, they become veterans as they fight and survive.
In the ancient world, armies generally hired their archers from woodsmen, hunters, and farm boys who had been using a bow all their lives. Therefore, accuracy was not their big problem - the military issue was just getting them to march in a straight line, and not break and run when things got hot.
I didn't said accuracy was a problem for bows, just that it required hard training. It takes years to train a never-miss marksman with a bow but once they are proficient, they achieve a good accuracy.
And as farmers and villagers in medieval age (feudalism?) weren't allowed to carry military weapons or to hunt in their lord's properties I don't think every villager was proficient with bows. So on, hunters had a special permission to hunt in their lords properties and helped him when he was gone to hunt. I think in a 100 people village (50% male), a maximun of 10 would be hunters IMO as fields&cattle demanded a lot of people.
I'd compare it to man-at-arms and farmer-levies: man-at-arms are trained and more effective but a Lord has tons of villagers to create levies. A Lord has less trained archers with a higher rate fire but has tons of farmers with crossbows that shot slower.