To the question of if you should pro-actively trap varmints to keep your local area free of them and the danger they impose? It depends. Almost all danger from coons arrives at dusk and ends at dawn.....which coincides with same hours the birds are in the coop and on the roost. If you have done your part to build sanctuary that protects them at night, trapping is not needed. They can be stacked up 3 deep, but if they can't get in to do harm, they are no threat.
But if you have holes or weak spots they can breech, they will get in and wipe you out. You can try to thin the herd by trapping, but you will never get them all, so while losses will be less, you can still expect trouble. When any one coon or varmint has success, they return time and again until you get the varmint or they get all the birds. Battle of wits and skill, and they are really, really good at it.
So question for OP.....what have you done with these cage trapped coons? Dispatched or relocated?