One of the possibilities that people inevitably raise as to why Houki resembles Nuriko is that she's actually the reincarnation of either Nuriko or Kourin.

Well, if you believe that tine is linear, than this idea doesn't make a whole lot of sense. Nuriko/Kourin couldn't possibly be Houki, since she's too old to have been born when Kourin died (and definitely when Nuriko died). But if you don't believe that time exists, and if you believe that someone can be reincarnated within the same time span as another incarnation, then hey, it works.

Suddenly, Houki becomes much more interesting. Rather than just being Hotohori's wife, she possesses the soul of an established character. Unless she has past life memories, she herself will not realize the significance of her circumstances. She probably feels fairly marginalized, considering her sudden and brief marriage to Hotohori and the fact that she so resembles Nuriko. Ah, the irony.

And what if she does have past life memories? That could be interesting...

Of course, if it is possible to be reincarnated at the same time as another form the soul inhabits, that could get very messy. For all we know, Nakago and Tamahome have the same soul! Nakago, Tamahome, and Mitskake! Before you know it, everything's a convoluted mess. But such is human life, in any case.