Scroll finials do serve a purpose and function. That function is in art & architecture. The purpose is to provide a decorative end to something. They have been used in metal arts for millennium. They were in use in iron work throughout Europe... and in bronze age work before that. But that doesn't explain why they became a characteristic of a particular type of firearm from only one region in North America.
Scroll finials were used in iron work by German immigrants in Pennsylvania, and by English immigrants in New England. But not on trigger guards in those regions. Why was it just the south? Who were the people migrating to the south in larger numbers? And why did iron mountings predominate in the south? When I look at the people, I see Scots and Scots-Irish. To me, that has to be the answer.
When we look to Pennsylvania, we see the similarity of the rifles produced there to those produced in Germany (and surrounding areas-like Switzerland). We see the German names of those who made these rifles. We conclude that the rifles from Pennsylvania evolved from those made in the German regions.
I'm not making the claim that the Bean family "invented" or single-handedly "developed" the iron mounted Appalachian rifle with scroll trigger guard. I only use them as an example of how Scottish immigrants in the south might be the answer to explain the unique style of rifles being produced there.
According to Jerry Noble in his book "Notes on Southern Long Rifles"...
"The Beans are descended from the McBain clan of Scotland." "We first find the Beans in Northumberland County Virginia. Old Wm. (William Bean) was born there in 1673, his brother, John, in 1682." "Many of their descendants were early settlers in Tennessee, Georgia, and the Carolinas."
The first white person born in what today is Tennessee was, in fact, a Bean.
He goes on to say...
"Wm. I (William Bean the 1st) was born in Northumberland County Virginia in 1721. He was in Halifax County by 1747, then on to Pittsylvania County in south central Virginia by the 1760's. He moved to what is now Tennessee in 1768 or 1769, being one of the first settlers there.Some sources say he was the first. He died there in 1782. Wm. I was a gunsmith and taught all his sons the trade, according to several sources."
If my memory is correct (I'm not betting money on it though) the earliest engraved date I can find on an iron mounted rifle with these Tennessee/Appalachian features is 1818. The Joseph Bogle rifle (also a Tennessee-made rifle) was made before his death in 1811. While that rifle doesn't have the scroll guard or Banana patchbox we typically associate with the school, it's still iron mounted and relative to the conversation. Joseph Bogle was also of Scottish descent. He was also related to the Beans by marriage.
William Ivey's book "North Carolina Schools of Longrifles 1765-1865" has a photo of an iron mounted rifle of the Bear Creek NC school attributed to gunmaker David Kennedy (1768-1837). It's not an Appalachian school rifle, but it is Iron Mounted. Another (brass mounted) rifle by David Kennedy has the engraved date 1807. According to Jerry Noble regarding the Kennedy's... "Early Kennedy's left Ireland in the 12th century for Scotland. They were in Pennsylvania before the revolution. Alexander (father of David) bought an interest in the gun shop of Wm, Williamson at Mechanics Hill, North Carolina shortly after the war and expanded it."
It is my belief that the iron-mounted Appalachian/Tennessee style rifle with scroll trigger guard and banana patchbox was fully developed by 1815. And I also believe it was developed by Scottish (and Scots-Irish) immigrants to the Appalachian region of the American south east.
Oh... and those feather holes between the trigger guard and toe plate that people have mentioned... take another look at that Highland pistol. The knob between the rams horn scrolls... that's a vent pick that screws into a hole. Maybe that's where the Southern "feather hole" evolved.