The fact that commutation can fail makes a huge difference in the whole patch
formalism. It may be possible to create a formalism in which commutation always
succeeds, with the result of what would otherwise be a commutation that fails being
something like a virtual particle (which can violate conservation of energy), and it
may be that such a formalism would allow strict mathematical proofs (whereas those
used in the current formalism are mostly only hand waving “physicist” proofs).
However, I’m not sure how you’d deal with a request to delete a file that has not yet
been created, for example. Obviously you’d need to create some kind of antifile,
which would annihilate with the file when that file finally got created, but I’m not
entirely sure how I’d go about doing this. So I’m sticking with my hand waving
formalism.