I had forgotten that Kagome can see where the jewel is and, moreover, can purify it as well. I think he wouldn't be able to gather all the fragments alone. She's so worried about InuYasha that she can't even enjoy the meeting with Houjou, who is such a sensitive and kind boy, the complete opposite of InuYasha. I can see what the author wanted to play with here, that we don't choose who we love. She manages to leave the encounter and return to the well, where her thoughts don't stray. And ends up back in the Feudal Era. Shippou was very happy. He's so cute.