I'm not advancing it as conclusive proof of abiogensis, I am merely advancing it as conclusive proof that your probability objection is ill-conceived. Like just about everyone else who argues that things like abiogenesis are impossible, or that all the other examples of emergent order and complexity in the universe can't possibly have come about as a result of purely naturalistic processes, you seem to think you are somehow justified in stripping the building blocks of reality of some of their most fundamental qualities and then declaring them to be inadequate for the purposes of explaining the behaviour that we see. Maybe you don't realize you are doing this, but you are doing it nonetheless. And it's probably because you just haven't spent enough time learning about and thinking about the sorts of properties that it was necessary for matter to have to get to the point in the evolution of the cosmos where it was even possible for there to be life-supporting planets in the first place.
The information on the DNA is based on the binary defined by two distinct base pairs. This codes similar to computer memory (or vice versa) in that the on-off or (base pair1, base pair 2) implies bits of data. Computer information is only one type of information. Molecules like protein, are also a type of material information. This is different from computer style information but means the same thing.
As an analogy, we can take a picture with a film camera to record information in visual format. A picture is worth a thousand words of information. This pic can be scanned, digitized and compressed to be stored as a JPEG on the computer. It now looks like bits based on on-off switched. Both are information, but only one is digital with digital an approximation of the original. Black and white film is about 1 million pixels/inch, so any scan is an approximation. Digital is modern and seems stylish, but it is an approximation to reality information, since reality information microscopes to great detail.
The digital information on the DNA is actually compressed information, with loss, because although a gene expresses the sequence of amino acids in protein, it does not directly contain how the protein will fold, where the protein will go in the cytoplasm, its relationships and its function. The cytoplasm contains all this raw data, as dynamics molecules, with the binary data on the DNA a compressed version of this data; only tells use the sequence and nothing more.
The DNA information is like the thumb nails connected to your picture collection. It has a rendition that allows one to span through all the pics with speed. But the thumb nails lack the full resolution of the original within the cytoplasm. If we change the solvent, the thumb nail in the DNA does not know this and still sends the same protein; thumb nail.
Logic tells use the proper place for the DNA in the information hierarchy is more like compressed thumb nails that define the content of the cell. In terms of interface formation, the thumbnails come late in the process of information organization. One does not start with a thumbnail to generate an HD copy. This happens after the interface is set up. The original has to come first, from which the a thumb nail will be made. Evolution is about setting up the thumbnail interface so there is fast and easy access to the final HD pictures, which will take much longer to load.
Too much dependency on statistics tends to atrophy reason down to dogma. The dogmatic approach to the DNA leads to nowhere since it lacks info logic in favor of dice.