What's the problem with -0?
It conceptually makes sense for to negativ values to close to 0 to be represented as -0.
In practice I have never seen a problem with -0.

On NaN: While its use cases can nowadays be replaced with language constructs like result types, it was created before exceptions or sum types. The way it propagates kind of mirrors Haskells monadic Maybe.
We should be demanding more and better wrapper types from our language/standard library designers.