Here's my 2 cents
1)Coaching-Maryville always has decent athletes, but not near the caliber of your more urban schools.
2)Tradition-My grandfather played at Maryville, My Dad played at Maryville, I played at Maryville, and hopefully my son will play at Maryville. I spent every Friday night during football season at shields stadium from as early as I can remember until I walked off of the field for the last time. It was ingrained in my upbringing. In Blount County you grow up wanting to play for Maryville or Alcoa. That is not the case with the other 2 schools.
3)Feeder Programs-The coaches from the grasshoppers to the middle school are preparing the kids the right way. And it's not uncommon to see the high school coaches at those games rooting for kids that will one day be playing for them.
There are other factors I'm sure, but those three really stick out to me.