Excuse my ignorance here, but I don't see why that explains the reason for mainly using the C autopilot (and hence FCC). Unless you're saying that:-
The left FCC can only provide inputs to the left trim channel.
The right FCC can only provide inputs to the right trim channel.
The centre FCC can provide inputs to EITHER the left or right trim channel.
We could then see what the effect of a trim channel failure would be on autopilot trim.