A removable singularity should not count for the domain. I understand that the domain of f(x) is the set of x for which the calculations indicated in the formula for f(x) lead to a numerical value, say real or complex. The domain of x^2/x does not include 0.
In my view, FunctionDomain lets the system make some algebraic simplifications that do not always preserve the domain. From the point of view of algebra, p(x)/q(x)=a(x)/b(x) if p(x)b(x)=a(x)q(x), where a,b,p,q are polynomials. In this sense x^2/x=x/1=x. But q and b can have different zero sets, and p/q and a/b can have different domains. For abstract algebra, a rational function is not really a point function.
