There are some limitations to pasting masks as strokes. You don't have options like you do when working with masks.
You can't change the first vertex, which means you may get strange interpolation even from similar looking shapes .
Smart Mask Interpolation is not available for Paint Stroke Shape. You can cheat a little though because you can also copy and paste masks from AE into a paint stroke.
You still may get strange interpolation, and even though these are vector strokes, you can't clean up the intermediary strokes without pasting another shape.
If you find you want to paste masks as paint strokes a lot you may want to consider just using masks and applying a stroke effect to them.