...one made from deer skin would be prone to sagging and stretching and a lining would counteract some of that.
That's certainly been my experience with bags in actual usage, especially in wet weather. Put a little weight in an unlined soft bag, and your buds will start making jokes about bras for older women.
But I'd be interested to see if there's any correlation between liners and leather thickness in history.
I think you'll have to factor in the aging/durability characteristics of different leather thicknesses and treatments. The historical remainders may be obscured by a shorter life span of light, soft leathers versus heavy through the centuries.
We have tack in our tack shed dating back to the turn of the previous century. Some of the heavier leather is fine, even usable with some care and restoration. But there is one 50-year old pair of deerskin gloves (made em myself back then, and forgot them on top of a sill until recently), and they are pure waste.