I've fretted over this for some time, because leather is not without its issues. As skin, it contains high water-content flesh, yet repels rain. It is renewed from within, by the blood supply.
When we cure it, we remove the bio-degradable material, replacing it with bacterial and fungus-resistant products such as tannins. These are mostly vegetal, producing a workable leather, at the expense of porosity, opening the door to biological attack, or chrome-based, producing thinner, therefore flexible, strong leathers. Other methods exist, including the use of organic plastics, and hybrids such as latigo.
Historically, in addition to wood, hardening methods existed, summarised here: https://medium.com/@jasontimmermans/a-comparative-study-of-leather-hardening-techniques-16-methods-tested-and-novel-approaches-8574e571f619. Also, wood, metal and stone could be used.
However, some cop-outs also happened. From my growing interest in shoemaking, I've become increasingly interested in the use of skived materials, where essential centre strength in thickness is camouflaged by thinner edges, and this may be what you're looking at here. Historically, two classes of writing material attracted covers once the production became comfortable enough to become standardised page rectangles, namely papyrus and vellum. Paper was a side-effect of mechanised weaving, as waste and worn-out textiles were initially used, until a method using wood-pulp was invented in 1847. The first recorded use of the term cardboard is 1848.
When we look at the oldest books, we find thin wooden boards as stiffeners, often coated in leather, which interfaced better with a linen spine the signatures were sewn to. Later, as cardboard became more normal, this replaced the board, and cloth the leather.
To me, the use of other materials accelerates wear on the softer, and should therefore be avoided. But please note, these are only a grab-bag of ideas, not determined suggestions, as there's a number of traditions to work in, and I'm not out to force your hand, but open the door to wider thinking. At the same time, I suggested a purist approach:
Therefore, we might revert, being leather workers, to turning the sides after skiving them, or to edge-finishing them. We might consider a softer lining, too.