Um, it was the Interior Ministry that defeated Ashina. And the person most directly responsible for weakening Ashina is Owl. Almost everything Wolf does to damage Ashina was Owl’s manipulation.
Genichiro’s whole motivation relies on Ashina being doomed, and that was long before he knew who Wolf was. Ishin also explicitly knows that his shogunate is on the clock and makes little effort to save Ashina or himself.