(Warning: there are indirect spoilers here for the endings of both Katanagatari and Haibane Renmei.)

Author wrote (a while back):

Possibly the fear of spoilers is why nobody wrote how Togame pulled an almost exact Reki reveal. [...] Now the reveal being the same, the subsequent resolution was different. Reki was tested and passed, but Togame did not have that chance. Kuro is certain that she would fail ("I am glad"). I am not so sure. She pondered becoming a mother at some point, remember. [...]

I'm not as optimistic as Author is because I think there's a crucial difference between Reki and Togame in their respective situations. As I see it, Reki's test was to confront, accept, and then basically let go of her past in order to move on. The analogous test for Togame would be to not just consider a future after her goal was achieved (which is something she talks about with Shichika) but to give up on her goal, to let go of her obsession for her revenge, and I don't think Togame ever considers or talks about this.

(Togame herself says that she couldn't change and do this, although she may have been lying about that as she probably was lying about other things in her episode 12 conversation. Or, if not lying, not seriously confronting the idea because there was no point to it by that point.)

The counter-argument is that being faced with your test can change people. Reki had that opportunity and without it, well, she might have ended up in something like Togame's situation (tacitly drifting into a bad ending). She was after all only saved at the very last moment (and with outside assistance).