The class of maps considered here are skew products of the form \((x,y)\mapsto (T_{\alpha}x,y+\phi(x))\) on \(\mathbb{T}^d\times\mathbb{R}^d\), where \(\phi\colon\mathbb{T}^d\to\mathbb{R}^d\) is integrable and \(T_{\alpha}\) is the rotation by \(\alpha\in\mathbb{T}^d\). By construction the product of the two Lebesgue measures is invariant, giving a family of infinite measure-preserving transformations parametrized for fixed \(d\) by \(\alpha\) and \(\phi\). The main result here is that if \(\alpha\) is Liouvillian then ergodicity of the resulting map is generic, and hence ergodicity is generic in the skew products over rigid rotations.