Honestly I think people look at the fact that Kagome is the reincarnation of Kikyou the wrong way. I like to believe that Kagome and Inuyasha’s destinies/fates were bound to each other so tightly, that even before Kagome was born, her soul found its way to Inuyasha, but it didn’t work out because it wasn’t yet the right lifetime. Their love literally transcends the passage of time, but backwards. That means, it goes even further than just the fact that Kagome travels through the well to be with him. When Inuyasha says that he was born for Kagome and that she was born for him, it implies he is meant to be with her in the life she’s currently living.
I see again and again people say that “Kikyou loved Inuyasha so much that her soul came back to be with him” but frankly I just can’t see that as true. What Kikyou wanted more than anything was to be a normal girl, and while she may have loved Inuyasha, her love for him was never unconditional. She wanted to change him into human for petes sake, I really doubt that kind of love would have stood the test of time.
I think the important part to understand here is that soul=/=person, at least in the Inuyasha-verse. The entire series is there to establish that Kagome is not Kikyou, and not just because shes born in a different time, but because her fate/destiny is separate from Kikyou’s as well. Kagome may have inherited the soul that Kikyou had, but that’s not to say it was Kikyou’s soul. Soul I think in this case means more in terms of life force than it does likes/opinions/fate. I think those are specific to each life time.
tldr; Kagome didn’t come back for Inuyasha because she had Kikyou’s soul; Kikyou met Inuyasha because her soul would one day be Kagome’s.