"life will be found to involve islands of chemical stability. (This is speculation, of course, but I will stand by it as my prediction.)"
Your speculation would be more believable if we were living back before we knew the DNA data content of genes (i.e. long before the genome was mapped).
Data is something that does not depend upon chemical stability, rather, it depends upon the sequential ordering of stable chemicals.
Rearrange the DNA data in a gene and you will change the output form, even though the chemical compounds involved will be just as stable as before.
Ergo, the sequence of the data is more important than the stability of the chemicals.
Rearrange the DNA data in a gene and you will change the output form, even though the chemical compounds involved will be just as stable as before. Evolution and selection can occur at different physical levels. The lowest level I'm familiar with is the transmutaion of elements in stars. Next would be chemical evolution of molecules, ala Stanley Miller. If you deny that this can lead to RNA or DNA, that's your position, your speculation about the history of the Earth.
But if it can happen, then we have the possibility of self-replication.
Without knowing the history of earth in detail, anything said about the probabilities of this happening is speculation.