A terminally ill patient cannot recover, but is functionally alive. A brain dead patient cannot recovery, and is not even functionally alive. I realize this comes across as harsh, but if you’re intubating a brain dead patient, you’re just circulating air through a warm corpse. One demonstrates obvious interiority, the other doesn’t exhibit anything except basic reactions that will permanently cease within minutes, if unaided.

If you want to reduce it to ethics, based on the definition of braindeath, one case involves the legitimate moral quandary of whether or not (and when) to allow a thing to die. The other case has no such moral quandary, because the thing is already (definitionally) dead.

Whether or not we like doing it, our medical system depends upon us making valuations about human life, even if only implicitly. If we allocate resources to keep a functionally dead object breathing the way a human being does, we’re taking away resources from a human being that is alive. It’s not rational if you accept the axiom that a braindead human is dead.