The way I understand it, the reason for reincarnation is so the soul can learn through all of its lives. Kagome's soul has been purified through that learning and I believe that the only part of her soul that had the darkness and hate of a normal person was taken by Kikyou when she was resurrected.
What would have happened if the soul hadn't learned and Kikyou wasn't reborn?
She flew through the air on the back of the hanyou. She didn't know why but the bow and arrow fit comfortably in her hands. She called upon Kikyou to lend her the strength and knowledge needed to shoot down the carrion crow that had stolen the jewel. Power swelled through her and she pulled back the arrow and let it go. Light blazed around the arrow and it hit, disintegrating the crow. She had a strange sense of falling and hit the ground with an 'oomph.' Inuyasha was flat on the ground beside her twitching as purifying light crackled around him.
"Damn it, you weren't supposed to purify me bitch!"
The boy was in pain and she was sorry... but in a small part of her heart she believed he deserved it.
She started staying around Kaede more and more. Kagome felt a strong desire to protect the jewel and needed to learn more about her powers... but more than that she needed Kaede. Memories of her home in Tokyo grew fainter as the attachment grew and memories of Kaede's childhood supplanted those of Souta.
Myoga found Inuyasha one evening and informed him of someone's search for his father's tomb. Inuyasha's disdain for his parents seemed to reinforce some of her darker thoughts about his character. Still she hung on to her beliefs that he couldn't be that spiteful... she could never feel this attraction to him if he was.
Her heart softened when she saw how he was treated by his family and she cheered him on as he tried to take Tetsusaiga. And was surprised when it only came out for her. She was surprised again when Inuyasha declared that he would protect her, but the greatest surprise came when her heart denied that he would. Memories of crippling pain haunted her for nights afterward.
Urusue came for Kikyo's remains one night. That night everything came back as Kagome's powers rushed into her control and light up the sky with the purified remains of the witch. Inuyasha stood to the side amazed as everyone else. The villagers bowed but her eyes were only for Inuyasha. Only he recognized the coldness that settled into the formerly soft blue eyes. The cold eyes of the woman who had betrayed him.
She stared at the hanyou down the line of her arrow. The fool thought he could make amends by becoming human like he had promised her before. As if she would let him near the jewel after she remembered his betrayal. Her heart quailed for a moment. If only her memories hadn't been repressed when she had fallen though the well she wouldn't have to go through this again. She felt her resolve slip. Damn her traitorous heart. It was to blame for freeing the bastard. She reminded herself that he had killed her last time because of her tender heart. She wouldn't make the same mistake again.
He knew he was going to die this time. Kikyo's reincarnation literally blazed with power- the power she had fully regained along with her memories of her past life. She wasn't restrained by lingering memories of his devotion or her love. This time he was a demon that had hurt her little sister. Even as he accepted his impending death he wondered why she was betraying him once again.
The bow creaked with the strain and white light enveloped the arrow. A snap echoed through the forest.
The air was thick in the hut. Kaede was stirring the millet when Kagome came through the door. She stared at her in shock.
"Kaede, do not question your older sister."