I think Nev was also considering inserting the unused trailer footage of Maz handing the lightsaber to Leia into Rey’s vision. It would be played in reverse to make it seem like Leia is handing it to Maz and then there would be an AI line from Leia basically saying something like “Keep it safe, old friend.”
Now, as for why Leia got the lightsaber, maybe she only happened upon it when Luke was already in hiding. I dunno, I suppose it’s better than it ending up with Maz inexplicably and she never even considered returning it to the Skywalkers (over the course of 30ish years) despite being close with Chewie and Han.