I also agree, that the author probably not meant to establish an axiom: The axiom being established, while not having any support right now, does seem like something we can reduce in the future. The author also uses the word "currently" in their axiom, which contradicts axioms (or is temporal axioms a thing?).
I think the author merely meant to establish the scene for the article. Something I truly appreciate.
"unprovability" is not a property that it is necessary to prove to pick something as an axiom.
There is generally a project to reduce axioms to the simplest and weakest forms required to make a proof. This is does result in axioms that are unprovable but does not mean the "unprovable" is a necessary property of axioms.
Uhm… no?
They are literally things that can't be proven but allow us to prove a lot of other things.