The thing about Kagome getting stuck in the Feudal Era vs Inuyasha getting stuck in the Modern Era is that, whille I wholeheartedly believe they would both choose to leave everything they’ve ever known behind for the sake of being together, Kagome being the one to do so was the right decision, both from a storytelling and from a character developmente point of view.
It just makes way more sense because, between the two of them, Kagome is the one who had more things to lose. Her choice carries a heavier weight, higher stakes. Therefore, it is more meaningful. And she had a harder time making it than Inuyasha ever would.
Not to mention that, on the other hand, Kagome fits in the Feudal Era like a glove. Perhaps because during the series she practically lived there already or perhaps because that was always where she was supposed to be, in the end of the day. But she belonged there. Inuyasha, I think, would have a lot more trouble adjusting to the Modern World. Not only because of his appearence, of who and what he is. But also because of bureaucracy. And technicalities. And our crazy modern day to day routine.
Besides, the symbolism and character growth of it all is exquisite and most often than not we tend to overlook it: if Inuyasha had choosen to stay on her side of the well, that decision wouldn’t be unthinkable to someone like Kagome. She’s not a strange to love and how much it affects and changes people. And it wouldn’t be much of a sacrifice for Inuyasha to say goodbye to a world who had always despised him to be with the first person in years to actually care about him.
The only things he had to took in consideration were the fragile hope that maybe, just maybe, he had finally found a place to belong with the friends he made along their journey and the beacon of acceptance that came with saving the world. Sure, it would be a shame to let go of that now that he had it. But she was the main reason he even got that far, anyway.
But at the beginning, Kagome was a bit spoiled. She was raised surounded by friendship, comfort and people who loved her unconditionally. Her life was way easier than average. However, at the end, she gave all of that up for a world of hardship, danger and uncertainty when she still had the option of ease, safety and sticking to what she knew.
And she did it mostly to be with a boy who had spent his whole life being told and thinking of himself as worthless and unlovable.