Before revision:  As a consequence of the latter, several problems would have quasipolynomial kernels, including Edge Multiway Cut, Group Feedback Edge Set for an arbitrary group, 0-Extension for integer-weighted metrics, and Edge Multicut parameterized by the solution and the number of cut requests.
After revision:  As a consequence of the latter, several problems would have quasipolynomial kernels, including Edge Multiway Cut, Group Feedback Edge Set for an arbitrary group, and Edge Multicut parameterized by the solution and the number of cut requests.