The saga of "straight" lasts could fill a volume on its own. Suffice it to say, like heel-history, there's more misinformation in print and on the web than au currant research. Regarding any of it, it's difficult to make broad sweeping generalizations that hold water for every culture, region, and age--no simple answers.
Except for a few 1st-3rdc. Coptic examples, I'm not away of any "straight" (lasted) footwear (both shoes made on the same symmetrical lasts) until c.1580-1600, concurrent with the introduction of heels. "Straight" lasts became a popular solution to a fundamental economic problem--after heels come in, lasts were now needed in no-heel (still), low-heel, medium-heel, and high-heel curvatures. If they stayed with pairs of L&R lasts, as were used to "forever", the multiplicity of lasts would have become enormous. One symmetrical last could serve for making both shoes, thus reducing by at least half the number of lasts needed!
Going by archaeological examples again, even after the introduction of "straight" lasts c.1600, the shoe uppers and their fastening methods remained distinctively L & R until the very late 1600s, and well into the 1700s in some cases. IOW, the "straight" last resulted in a symmetrical sole shape when brand new, but after a little wear the shoes became R & L in wear.
By 1767 (see Garsault) there was a fad amongst some Europeans to preserve the symmetry of the sole shape by switching shoes (NB--only feasible with symmetrical uppers/fastenings which were not universal), which was decried as ruining the shoes, and miserable on the toes (which is easy to see). Other contemporary authors (i.e. Peter Camper: 1781) dismissed this as nonsense, as apparently the Dutch "peasants" never wore "straight" footwear all along. I know you didn't raise the whole rotating-shoes-like-car-tires to make them last longer hoary chestnut, but it is popular too, beware. If one had to go to court and prove, with either archaeological or written proof, for swapping shoes 1600-1800, they'd be hard pressed to find any. Only occasional local hints, like Garsault et al.
During the hey-day of "straight" lasts I've never found them called "straights"--they were just called "lasts", because that was the only shape known/remembered. The first mention of "crooked" per se lasts and their superiority was, in Rees (1813), after R & L lasts were revived as "the latest European fashion" in the 1790s. From there things get muddied.
"Straight" lasts were cheap to make, and it was simpler (cheaper) to make straight uppers patterns than R & L uppers, so "straights" continued for the cheapest footwear, especially factory production, right though the 1920s. Right and left shaped lasts, cost more, but fit neater, and tended to be used for better grades of footwear from c.1800 onward (to today sort of).
It's 1819, enter Mr. Blanchard, who patented his lathe for turning shoe lasts "and other irregular shapes in wood"--his patent papers and patent model show a shoe-last-turning lathe--not gunstocks as popularly claimed. The first commercial buyer for his new gizmo was; however, the U.S. g'ment, and the lathe was only then modified to turn gunstocks. The weakness in Blanchard's lathe was that it did not adjust to grade from one size model to other sizes. In 18(57?) (Mr._____?) patented the pantograph attachment for Blanchard's lathe, for grading, and only then do machine-turned R & L shoe lasts take off in huge quantities in the U.S., Europe following. Again the U.S. military were the protagonists--the U.S. Army STOPPED accepting straight-lasted footwear from contractors in 1851, necessitating the sudden (huge) need for R & L lasts cheap. Similarly, in 1861, at the outbreak of our Civil War, MacKay, who previously could not get any buyers/backing for his chain-stitch sole-stitcher, got the Army to reluctantly accept MacKay sewing (as the least desirable construction BTW), and voila his machine went into production.
Anyway, I know I wandered off topic here, but too much caffeine this a.m.