So I reread the chapter, and this time I got a different impression of Sesshomaru's actions.
On
page 13, Sesshomaru has this line after he picks up his sword again. "Naraku, I already have the answer." It now become clear to me what he means, and also the look on his face is very telling in retrospect. After he says that line, he tells Inuyasha to ready himself, and then Inuyasha breaks/absorbs Tenseiga.
By that line, Sesshomaru meant he had the answer about whether or not Inuyasha was Tessaiga's true successor. When he thought he beat Inuyasha, he left him in the Meidou. When he saw Inuyasha's power was sucking up the Meidou, he realized he was wrong. Then, he reclaims his sword, and knowingly and willingly allows Inuyasha to absorb it.
It's just like Totosai predicted, that when Sesshomaru is willing to let go of his sword, he will surpass his father. This wasn't a defeat. This was character growth.
I don't know why I didn't read it that way the first time. Probably the shock/upset of seeing Tenseiga broken didn't let me think things over well enough. But knowing it was Sesshomaru's choice makes it much easier to take.
Sure, I still don't want Sess written out, but at least now maybe he can walk away from this battle with his ego a bit less bruised.