I do prefer using small leads with chod rigs and don’t feel that they hinder the hooking properties of the rig.
I want the lead to lay down gently on top of whatever it is that I am fishing over. I also want to cause as little disturbance as I can.
Fishing in this style often means being mobile and reacting to what the fish do.
The last thing you want is to crash three big leads into an area that the fish are happy feeding in.
A large lead will give you more hook pulls too, in my opinion.
That large weight around the carp’s mouth has a tendency to pull the hook out, while a smaller lead, doesn’t apply so much pressure and is much better for landing fish.