McCallie can host the game wherever they want but I think you are confusing the issues. McCallie stadium, like Baylor, has a capacity of around 6000, and the only people that will show up for the game are those that have tickets ahead of time. No one else gets in. So, the logistics of 10-13,000 is irrelevant since the logistics are the capacity of the stadium.
Now, one might argue that all 10-13,000 that want to see the game ought to be able to see it, and if that is one's point of view, then Finley is a great venue. But if you want a great atmosphere with deafening noise and want to take advantage of a home field advantage (as Baylor does), then hold the game at McCallie. I don't think logistics are the real issue here. I think its the tradeoff between great atmosphere and access to all.
One last word. I was at the game at Baylor when Baylor broke the streak and that was the single most exciting sporting event I have ever attended. The atmosphere was movie-like and pure "Friday Night Lights".