I added our vote to this issue: RH-65521 SubD Symmetry: Make reflection plane editable after Reflect. I think it asks for the same thing.
I don’t understand your request for “has the option to have normal alignment with the symmetry plane”. Reflect is exactly a normal reflection, so all edges crossing the reflection plane without a vertex on the reflection plane are normal to the plane. If you do not want vertices on the reflection plane, you need to delete them; they will be easy to select in a top view.