It's a big region that's seen a lot of historical change. Pronunciations differ . . . between insiders and outsiders, but also between subregions . . . and pronunciations change over time. What you post about represents truth, but not everyone's truth. Not even everyone who lives in or has roots in Appalachia.
The region has seen a lot of historical change, but the pronunciation of Appalachian with the "latch" or "ă" sound has actually been fairly consistent in the core cultural areas. Its origins come from 16th century Spanish phonetic transliteration for the Apalachee Muskogee tribe, which lived in what is now northern Florida. The Apalachee language does not have the "ā" sound found in the northern "App-uh-LAY-shun" pronunciation of the mountain ranges. Moreover, this "ă" sound is also present when talking about the "Apalachee" and "Apalachiacola" American Indians. FWIW, one would not call them the "App-uh-LAY-shee" tribe. The "sh" sound also absent in the Spanish pronunciation of the mountains. They are the Ap-uh-lătch-ee tribe, and Spanish speakers say (and I approximate here) "ă-pa-lă-tches." Even when looking at older maps, for example, one can sometimes find a more phonetic spelling variations, such as "Appalatchan." French Huegenot explorers in 1564 identified the mountains as the "Montes Apalatchi." Likewise, one Spanish prisoner of Sir Frances Drake in 1586 also wrote of them as the "Apalatchi" Mountains. How the cultural core of the Appalachian Mountains pronounces the word is remarkably consistent with this historical prounciation and etymological origins.
In contrast, the App-uh-LAY-shun pronunciation came much later, by comparison, but not from the cultural core regions of the Appalachian Mountains that identifies with "Appalachian" as both a physical and cultural region. How the "locals" in the northern mountain reaches having been saying the word is fairly new, as they didn't refer to the mountains they inhabited as the "Appalachians" in the first place. Historically in America, the northern section of the Appalachian mountains were primarily known as the Alleghanies for a
long time, while the southern ranges were always known as the Appalachians. It was only until later that Appalachian became the name for the entire mountain range, with sometimes Alleghanies being considered the "proper" name for the mountains at some points, particularly by non-Southerners. IME, a fair number of Northerners I have spoken to still think of them as the Alleghanies and would never think of themselves as "Appalachian," particularly since the term conjures negative stereotypes of rural white poverty, uneducated hillbillies, etc. For example, one friend from New York I spoke to said that the mountains in
Last of the Mohicans didn't look like "[his] part of the Alleghanies." When I asked if he considered himself "Appalachians" he likewise retorted, "Why would I? I'm from the Alleghanies in New York."
"App-uh-LAY-shun" is an invention. It is a pronunciation that trail organizers from the northeast in the early 1900s thought sounded more aesthetically pleasing than the local pronunciation of the core and southern regions, and many people outside the Southern Appalachias followed suit because of the assumption that we don't speak proper English and therefore must be wrong. For the past one-hundred years the southern Appalachian mountains and its people have been identified as a "social problem" to be "fixed." We have been treated as an impoverished uncivilized people in need of saving by people who know better while also repeatedly derided as a cultural backwater and the butt of many jokes and negative stereotypes. And with Outsiders' desire to "save" us also invariably came "App-uh-LAY-shun" pronunciation with them. Our English was wrong. Our dialect was wrong. Our pronunciation of Appalachian was wrong. In short, our culture was wrong.
If the political power of names and the desire to "save" barbaric, uncivilized lands sounds familiar, it's because it's not that far removed from Edward Said's argument about Orientalism, albeit here happening in the backyard of the Americas. The pronunciation of "App-uh-Latch-uh" is also an act of political resistance against our cultural erasure. This reality has been picked up by a fair number of professors and scholars of Appalachian Studies. Our pronunciation has increasingly become the preferred pronunciation in these circles for that reason.
People are welcome to tell me that there are many acceptable pronunciations of "Appalachia," but the pronunciation you use communicates a great deal to many of us in or from the Appalachian cultural core. It is a cultural and political signifier regardless of whether you never heard it pronounced any other way than what you grew up with.