They had to make the most of what little Carrie Fischer footage they had, and making some sort of point to surround Leia handing her the saber was a way to do that. And having Leia’s own saber represent her reinforces that idea.
Although I wish it were a different color as to not be indistinguishable from Luke’s.
They did. Leia’s is blue and Luke’s was green. This is their father’s saber, which happened to be blue as well. Those sabers really don’t represent brother and sister, but father and daughter. Luke’s saber has only been seen in flashbacks.