What about the distance? If you only have one, distance quickly become huge.
With, e.g., one for each theatre, distances are reduced.
Why is the distance from the supply source important? If I understand it correctly, it only determines which units will be prioritized (those that are further away from the center). It is much more important where the supply itself comes from. For example, if you have your industry on the border, on the supply line, it will funnel the stuff directly towards your units, no problem.
Now, I had experiments with this stuff, and I found that if the IC is not directly on the supply line, then it will go back first, and only then go to the units. That is stupid, and I can't imagine why it is so. They should work exactly like ports, sending stuff to the units, and only when noone wants them, send it to the depot. (By the way, in my humble opinion, there's absolutely no need for any supply centers... They do nothing, only serve as a reference point...)