Shadows are extra baggage but it’s not because the property is saved as part of the scenes. If shadows are on, the graphics card has more to calculate and so, yes, the redraw time would be longer.
In your model there was no reason I could see for not saving the axis positions.
It wouldn’t be that way by default. The default state for all of the scene properties is that they are saved and updated. Might want to check your default template to see if you turned off the Axes Location there.