...... snip........ Again, I refer back to my analogy of dropping a marble from up high, letting it pass by a fan on the way down. I won't disagree that there may be a VERY short period when the bullets lateral momentum remains uncorrected, leaving the bullet flying non-parallel to the bore....but as long as we're guessing, I'm guessing that effect is very short lived before the bullet is again parallel to the bore but on it's new path to the target.
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What exactly is the force, beginning at 500 yards at the point where the near wind quits, which you claim would return a bullet back to a path parallel to the bore once it is traveling on a nonparallel path? Look at it another way. Take any bullet path and ask yourself why it would suddenly change it's lateral path as if acted on by a wind, but without any wind present? In other words, if the near wind pushes the bullet into a curved path and then that force suddenly stops, wouldn't Newton's first law, which says in part ".........an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
In other words, at the 500 yard mark, the bullet is traveling at some lateral angle to the bore. What would make it then reverse this trend and turn to parallel the bore. Why, if there is no outside force, would it not continue at that angle, whatever it is, for the next 500 yards thereby taking the bullet further and further away from the POA?
Or, consider this slightly different situation. Set up a piece of steel at an angle of 45 degrees to your bore at some distance, say 500 yards. If you shoot toward this piece of steel the bullet flies nicely at first toward the target, again we're ignoring the effect of gravity and the much smaller effects of spin drift, and other minor factors. When the bullet hits the steel, it flies off laterally in some direction, let's say 45 degrees to the bore for argument's sake. That's similar to what a near cross wind does, but it happens all at once right at 500 yards where the steel plate is. Now once the bullet is flying on this new path, what force would tend to bring it back to fly parallel to the bore during the last 500 yards? None, the drift just prior to the steel is zero and the drift right after the steel is one yard laterally for every yard down range. Assuming there's enough energy remaining to travel 500 yards after the steel, the bullet would impact the target with a 500 yard lateral deviation, ignoring the fact that in the real world gravity would likely end the experiment early, but you get the idea.
In short, if the bullet is deflected from a path parallel to the bore onto a new path at some angle to the bore, when the deflecting force stops, the new direction will be maintained and the lateral error will continue to increase just like it does when you don't aim properly. If you fire when your rifle it is aimed to the right or left, the resulting error might be hardly measurable at 3 yards; in other words, even a pretty bad aim won't kill your chronograph. But down at the target that angular difference will be quite apparent and it will score worse and worse as the distance to the target is increased.
An additional thought experiment which you could actually conduct if you wished is this. Rather than drop something past a fan, set up a fan blowing across a ping-pong table. With the fan off, roll a marble from one end of the table to the other. It should roll in a nice straight line. Next with the wind blowing across just the first half, roll the marble again. It will follow a curved path downwind and when it rolls clear of the wind at the halfway point, it will NOT return to the original path. It will continue in a straight line (because there is no longer any lateral force) on the revised path which will be at some angle to the original direction. Depending on how long your table is, how strong the fan is, etc. that angular error will result in an increasing lateral difference between the POA and the POI, to use shooters terminology, as the marble continues along it's way.