OK, the second reason for the "division line" is....

[Nevadaref]

Sorry, but you are mistaken. The original intent of the rule, which was to make it easier for the defense to steal the ball, is perfectly in line with the three situations that you have listed.

In all three situations, the offense gets punished, but the defense does not.

The rule was put in to increase the likelihood of a turnover and that is exactly what happens in all three of the cases that you have cited.