giving the constant 20mm offset between the POA and POI at every range...
The image below considers your side mounted scope. If your zero distance is short, then the effect of proximal crossing of the POA and POI planes means that a
20mm offset on the rifle is 40mm at twice the distance beyond the zero'd distance.
I realise that would not have a practicle application for hunting or military purposes where rifles are probably zero'd at 200m. So the offset would only exceed 20mm
beyond 400m. i.e. it would remain 20mm
or less for all practical distances.
But it remains a consideration for those shooting at 500m or more
based on a 100m zero. But...
...the side-mounted scope is not the modern day shooter's typical challenge.
In the scenario of your second offset image, your minimal offset statement
only holds true where the scope vertical hair is perpendicular to the horizon. So it requires a rotated scope mounting
married to an exactly equal cant when the rifle is in the shoulder. That statement is true, but
unlikely.
More likely is a small scope deviation from truly perpendicular and an unknowable and possibly variable user-applied rifle cant at the point the shot is taken. Per the OP, I am striving to eliminate the error introduced by the former to lessen the impact of the latter on POI.
A flickbook approach to your second image shows the POA and POI planar divergence. Once again, that divergence is only likely to affect longer shots, agreed, but it cannot be a constant value either.
