You more seem to have faith--probably better to say "confidence"--that such an explanation is impossible.
To the extent that Neo-Darwinist theorizing restricts itself to physicalist/materialist presuppositions, it cannot explain the emergence of life. Period. End of story.
You hope. This is the second time you've referenced Kahre's Law, which I hadn't previously heard of, so I went looking for references to read up on it. And I found a paper (PDF) that acknowledges the "information paradox" you describe, but says "We show that the resolution of the fundamental information paradox may lie either in the chemical evolution of inheritance in abiogenesis, or in the existence of an autonomous biological principle allowing the production of information beyond physics." Further,
If our results will be confirmed, it will turn out that biology cannot be reduced simply to physics, since its genetic, algorithmic and symbolic information content is much higher than that of physics. Our proposal not only allows biology to follow its own, and, necessarily, autonomous first principle not derivable from physics, but allows also to approach biology from a viewpoint that can make theoretical biology to develop into a science with exactness almost reaching the exactness of physics.So for this scientist at least, the information paradox is not the end of the story, but rather the start.
Looks to me that Kahre — though he acknowledges a potential "either/or" situation — has decidedly come down on only one side. And it is definitely not on the side of abiogenesis as an explanation of the emergence of life.
Please read his statement — carefully — again.
Also please note: We are speaking of Kahre's LAW, not Kahre's "hypothesis," or Kahre's "theory." Science is very careful about attributing the status of a "law." It goes without saying (perhaps) that a LAW is a stronger thing than a hypothesis or a theory.