HBK-79
War Child
High quality cables, well-organized layout of the system, and he's not using all the pedals at once.
Remember, when you use a switcher, only the pedals (or rack units) that are switched on are in the chain at any one time. When you think about what Edge uses most of the time in his main chain, he really is only running 1-3 pedals plus a 2290 and (usually) the SDD3000. He may switch different units and pedals in and out of the chain by changing patches or switching on or off individual effects, but he's not running everything at the same time.
Hence, no tone sucking.
Again, it comes back to the switching system he uses.
By "not running everything at the same time," are you referring to the thought that not all individual stompboxes/rackunits are on?
I always thought that you could have all the pedals turned on at the same time, but you could disengage any loops that contain pedals that are irrelevant to a song. Like what Gerry demonstrated.
Thus, you eliminate the tone sucking.