A fair viewpoint if it were congruent with the science behind neuroanatomy at all. The idea that brain activity is equal and/or autonomous in both hemispheres and as such a human brain could function in such a state is fantasy.

The idea that the brain is the seat of consciousness is a logical inference and an observable phenomenon (try having a conversation with a corpse). Perhaps if brain transplant ever was successfully performed Parfit's theory may be observable but I expect it would have disastrous consequences, I don't think I have to explain why chopping out half a brain and put it in someone else's head is probably a bad idea.

It has been observed and documented that some transplant operations seem to pass on donor's health issues (strictly medically speaking) to the recipient.
Perhaps a brain transplant would have a similar reaction. Even so, I can't see this being much more than a primitive and naive experiment if it was ever conducted.
The physiology of the human brain is a myriad that we are starting to comprehend. Our brain is a delicate instrument and must remain intact if it is to function to its best ability. As such, any trauma or disruption is likely to do some harm to it, such as surgical intervention.

Basically I think this idea is conjecture from a philosopher that has an insufficient understanding of the fields of science is relevant to. Yes, I understand that as a philosopher just posits the idea but the science of his concepts is important and the reality of performing such a procedure is relevant to the concept he has put forward.
What use is philosophy if has no bearing in the world we live in? The grandeur of its imaginings are lame when introduced to the wondrous complexity of life itself, an existence that makes its own terms and abides not to the often naive inferences of human beings.