Apparently they do increase biodiversity, water quality and so on, unlike mink which just eat native wildlife. I think they are effectively still native (as the time since they were made extinct in the U.K. is fairly short in evolutionary terms).
There are plenty of things such as some deer species which are non-native, or at least have had their native predators wiped out, which cause huge destruction.
Not to mention moor burning, which probably isn’t a good thing from the POV of downstream flooding among other things.