That's straight back to arguing for a universe that is not logically consistent. In which case you lose the argument by definition.
The argument (woo-side QFT equivalent) was logically consistent, proposing of form of symmetry. It was invented out of whole cloth, yes, and in no way offers any means of testing for evidence. Fantasy yes, yet logically consistent and a valid example of a woo claim unfazed by QFT.
Your mistake lies in thinking that only positive claims require proof. Negative claims do, too. To claim
proof that there is no afterlife, one needs to backdoor elements that do not pertain.
That does not mean one ought to believe in the notion. The positive claim that there
is an afterlife, when made, is one that can easily be dealt with, from Occam's razor to QFT, whatever,
depending on what exactly is claimed as evidence in the natural world. Until such a claim to concrete evidence comes into play, all woo is merely rationalized fantasy that science ignores, having better things to do.
What we have is a situation of no proof either way in
general terms, and myriad ways to disprove any
specific claims regarding an afterlife if and when they intrude on science.
I am a great fan of Carroll, yet am aware of his tendency to generalize when presenting for the public things that he later qualifies in written discussion. His ideas are all sound.
It's the thread and the runaway claim to a definitive sweeping proof of a negative that is out of line.