The neglected timeline of Inukyo every Inukyo wants to be respected for it is valid, is that Kikyo was making Inuyasha more human, more tame, more domesticated, to the point that being human permanently did not scare him like he previously describes being human made him. He felt safety for the first time. His temper decreased significantly because of her. He no longer said mean things or tried to put her down. He learned how to be considerate of others feelings, first with her.
There is unsung moments of tenderness between inukyo in these events
There is a drastic change in behavior and expression with Inuyasha in particular.
Kikyo is described to have a calming aura, that put others at ease by Kohaku. She soothed Inuyasha most of all.
So while the tragic love song may be filler
...it had to have gotten some of it right.
If you think Inuyasha has to be hotheaded brash, and emotionally immature to be himself, I remind you it was Inuyasha only that understood Kikyo’s heart truly, and she is the most difficult character to empathize with.
