There's a really good answer to all your questions... it's called "fashion".
During the 17th century, continental arms were more highly decorated and more advanced that English made arms. By the middle 18th century The English had copied the better made continental styles and were on par with continental Europe. By the late 18th century, continental arms styles became somewhat more static, with less advancement. The English maintained there advancements and surpassed continental Europe. In some parts of America the styes stagnated. More progressive gunsmiths (and customers) followed the better arms coming out of Europe at the time... and those were made by the English. They simply copied the best that were being made at the time... but as artists... put their own spin on them.
You see the exact same thing with clothing fashion... cars... whatever. If there was a logical... scientific... cause and effect... reason for everything... then why do men still wear ties. There's no practical modern reason for doing so. Have you seen men stand up and have to button their dress coat... then... when they sit down again... they have to unbutton the coat. Stand up... button. Sit down... unbutton. Over and over. There's no "has to be a reason" reason for this. It's just fashion trends. We learn more by studying the trends than trying to explain them.
Setting aside engraving, finish etc, you are certainly correct that not all technical features have rational explanations. But some do. And sometimes the "fashion" as you say is actually the pattern of use, and the tech feature is a rational response. For instance, if there grew a "fashion" of shooting cross-body, then flat plates might morph into better-functioning crescent plates that anchored above the bicep.
Or theoretically the inverse could happen: gently curved plates might for aesthetic reasons become deeper and then for comfort's sake shooters started shooting cross-body, which allowed plates to become even deeper like some SMRs. This would still reflect a change in use. If everybody dug the cool schuetzen "look", they'd start holding rifles schuetzen-style whether they wanted to or not. There's no choice.
But it is unlikely that the crescent plate came first out of aesthetics causing everybody to switch style just to deal with a painful, irrational plate.
And since target shooters from schuetzen to today shoot cross-body, many with extended buttplate hooks, it seems pretty likely that American longrifleman had a rational reason for shooting cross-body and crescent plates followed.
What's completely implausible to me is that crescent plates were adopted for the "look" but jabbed into the shoulder pocket like a flat plate.
And sometimes tech features are not fashion but reflect lack of understanding. Americans might have overestimated the tech advantage of long barrels because they lacked chronographs, but then the barrels had a rationale other than fashion.
Fighter planes post-1945 don't have swept wings because it looks cooler. Guns are tools and design responds to how they are used, the state of technology, or other reasons.
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