I have figured out that SubMesh is not ment to be used in parallel and although MeshView is supposed to be used that way, it is currently not working. (See BoundaryMesh of MeshView in Parallel - #3 by LiborKudela).
The MWE provided at the top does not work in serial either… I still do not know why. It might not be meant for nonlinear variational problem.
Anyway I am going to try to find a workaround.