The survival of any bridgemen against archers firing from 20 feet away bothers me some too, but it's not a deal-breaker.
I think when we imagine the Parshendi shooting, we may see there being a thicker flight of arrows than is necessary. In movies, especially lately, arrows are shot in clouds that blot out the sun (see
Hero, 300, etc). But we've also established (or at least theorized) that the supply of arrows is probably not that great. We know that the bridge crews are subjected to direct fire, but the fact that the Parshendi don't have enough arrows to slaughter every crew that approaches indicates that the flights are probably only a few dozen at a time directed at any one crew, spread out over 20 crews of 40 or so men each.
Arrows don't fly like bullets, even over short distances. They can curve and twist, and a near-miss is still a miss. Several arrows might hit a single man, especially since the outer layers help protect the inner groups, so it might take a couple rounds before you've killed enough men to force them to drop their bridge.
So if you imagine the volleys being like a cloud of arrows, you're overdoing it. I don't think Brandon ever actually defines how many archers are amongst the Parshendi army, and not every Parshendi is shooting at once. It's still enough that the first few rows of any crew should expect to die, unless they've got an honorspren twisting the wind for them.