Your rate is low. A semi-decent archer (which most men were, practicing every Sunday after church) should be able to loose at least 12 arrows/minute. Most students (~80%) are able to do that, safely, after about 4 3-hour training sessions, 2 weeks apart. Admittedly, they're only using 30-40lb bows, and can only do it for 1 minute, but that's just lack of strength/stamina which comes from practice. A fair proportion can reach 15 arrows/minute, and a very few will eventually be able to get off 18/minute.
This is for shooting at a block of billmen, which does not require much in the way of aim. So long as you aim in roughly the right direction, and get your elevation and draw length mostly right, that's all that's really necessary.
For target shooting, most competent archers will be able to hit a 1m target at 20m >75% of the time, loosing in time with a 12/minute count.
At 12/minute your not going to be able fire again before someone 20m from you get's in range. Second 80lb is light on the light but useful end of a medieval bow. Also, their arrows where much heaver and less stable in flight than what most people use now days.
PS: There is something of an arms race with bows, if you use a 100lb bow and your opponents use 80lb bows you can slaughter them before they get into range. (Ignoring wind, and terrain issues.)
No, but that's why you aren't a lone archer on the field. You're in a block of dozens, and you're behind a block of billmen who stop anyone with a hand weapon (bill, sword) from getting anywhere near you.
If that fails, and someone is anywhere near 20m, you drop your bow and a) draw your own hand weapon, or b) more likely - run. Because if you're up against someone whose primary weapon is a sword, they're likely to be better than you and have more/better armour, so your odds are low. On the other hand, if you're up against a billman, your odds are basically zero.
I only put the accuracy for a 20m target because a) that's what we shoot at for practice in my reenactment group, and b) to demonstrate that most people can aim moderately at that distance while shooting quickly - they're not just pinging arrows off in any direction in order to get the rate of fire up.
As a longbow archer, your primary job is to put as many arrows as possible into a large block of men 200m-300m(-400m?) away before they get to the billmen you're protecting (and who are protecting you.)
This is for shooting at a block of billmen, which does not require much in the way of aim. So long as you aim in roughly the right direction, and get your elevation and draw length mostly right, that's all that's really necessary.
For target shooting, most competent archers will be able to hit a 1m target at 20m >75% of the time, loosing in time with a 12/minute count.