It's important to look at period-specific Gibson mandolin markets to understand the popularity of the scroll.
Historically, there was a ping of intense mandolin interest from the late 1800s to the end of WW1 during which Orville Gibson's mandolin work became socially popular among the well-heeled in the parlor and for community and university mandolin orchestras, similar to S.S. Stewart's work during the "classic banjo" period that predated the mandolin's musical period in time. Orville Gibson built his instruments either with or without the scroll. The more expensive instruments had them, they added visual appeal and balance and perhaps some physical balance along with the points that had recognizable utility value. The scroll on fine violin family acoustic instruments has actually been attributed to provide tonal differences, so there may have been some mandolin related logic for that. Most mandolins were played sitting, so the concept of putting a strap through the scroll wasn't a big influence, and wouldn't be until much later in the mid-1900s.
Once WW1 ended and the Jazz Period began in earnest, the mandolin could not compete for volume with the horns, jazz banjos and drums, and the semi-classical mandolin had begun slipping out of popularity, along with the 5-string classic-style banjo. By the time Lloyd Loar came along, Orville Gibson's influence in the company had ended and he had subsequently passed away. Gibson as a company hadn't made big commitments to jazz banjos yet and was looking for a way to keep their aging mandolin and meager banjo investments profitable. While a few notable period musicians would continue their work, the Jazz Period would eventually nail the lid on the coffin for both the semi-classical parlor mandolin period and classic banjo period in popular music.
At this time the mandolin in Gibson's eyes was still a semi-classical instrument. Mandolin was not widely considered a full classical instrument. Bluegrass didn't exist yet and wouldn't be strikingly popular until the mid-to-late 50s and even then interest in new Gibson mandolins for bluegrass would not inspire Gibson to listen to popular demand with its model designs for another 25-30 years. So Loar's mandolin design changes were made to appeal to the dwindling pre-WW1 semi-classical parlor-mandolin period players. In contrast, Loar's guitar designs were extremely successful and popular for this pre-electric Jazz Period because their tone and volume could penetrate better.
By the time the mid-20s came along, the Gibson company had fully invested in banjos and was successfully pressing them forward for Jazz, and the mandolin fell quietly into the background. Loar had left Gibson on less than pleasant terms and was striking out on his own endeavors, which unfortunately never reached into serious popularity or profitability. His time at Gibson was really a last-ditch stop-gap effort for the company as they switched gears in production to the jazz banjo.
So the scroll was Orville's design, primarily for visual appeal and balance for his higher-end instruments, but it may also have added some tonal differences. Loar may have specifically changed Orville's design of the scroll in various ways, but it still was primarily on the higher-end instruments. Unlike many other specific features, the scroll wasn't described in Gibson catalogs as being specifically a source of any different sound quality, but was part of the package with the higher-end instruments.
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