Since the debates are televised and reaches MILLIONS, the size of the "stadium" is not the issue.
Acoustics, lightning, sound controls, are probably more managable in smaller, more "homey" settings.
After all, the size of the CROWD in the room is unimportant......what's important in a debate is the candidates answers and responses.......which might get drowned out, with too much cat calling and whistling from unruly staduim mobs.
Surely security is also an issue.........smaller venues have better entrance and exit protection......and easier to patrol for secret service. After all,one of these men might be your next president.......and no one wants a repeat of Bobby Kennedy.
Another reason is simple......older people are more set in their ways.....and are probably well set in their thinking later in life. In Universities......you still have the chance to preach to fresh minds....and sway opinions to your side. It's fertile ground to recruit campaign volunteers........the voices of the NEXT generation. That's probably why universities are chosen........younger, engaged , enthusiastic live crowds, with the security of reasonable sized auditoriums that are easily protected....and usually quite suitable for the task of setting up 8 or 9 podiums or chairs or whatever, in a personal, cozy,tempature control, element-free setting..