It makes just about as much sense as him being a female Argonian
The Nerevarine is not supposed to be an exact replica of Nerevar, just of his spirit (hell, one could argue its his archetype thats more important than the actual soul). In fact, a major part of the prophesies is about him being foreign.
That is correct. And why would the Nerevarine necessarily be in House Indoril? As an outlander, you weren't born into it, so you would need to choose to join it, it must be noted that at first, most people don't actually accept you as a Nerevarine, even once the fact that you claim to be the Nerevarine is known, the Temple says that you're a heretic, and even once the Temple changes that stance, not everyone necessarily believes you are Nerevar reborn, and at that point, the player may already have joined a seperate house. Just because the Nerevarine is reincarnated from someone who was in House Indoril long ago doesn't mean that he'll automatically be accepted into House Indoril.
It's not like the player is litterally Nerevar ressurected from the grave, I think people would be even more reluctant to see someone like that as their savior, seeing as you'd be a skeleton, if not a pile of ash or bonemeal. If a skeleton walked up to you and said "I'm an ancient hero reborn to save the land!" would you believe that? The Nerevarine is a new person who presumably has the soul of Nerevar, and his choices and actions won't necessarily reflect what Nerevar would have done.