True. My personal answer to this is that I consider a "person" to be the processes that occur in the brain from which consciousness arises via some mechanism that is not yet well-understood, with the body more or less just being a vessel for those processes to occur in and for the consciousness to interact with the world.

And so my personal opinion is that the only real use for keeping a braindead body alive would be to keep its organs viable until transplantation, but I do understand that that is probably an opinion that is quite far to the materialist side of things.