Elon clearly wants go further in exposure and developing the school (increase the size of the operation, increase endowment, etc). No other explanation for these kinds of moves. They may be at the low end of the CAA right now, but before the CAA, they fit in the Southern Conference fine.
Belmont University is joining the Southern Conference soon. Their endowment is $108 mil. The Southern Conference obviously has a long history, but countless schools have gone through it. (Such as most SEC schools.)
College of Charleston also left the Southern Conference for the CAA.