I have BCP, LMB and BG in my pond....among others. It can be a delicate balance. The pond used to have decent bluegills 6-8", a great amount of 10"+ eater crappie (with some up to 15") and a nice mix of bass. Soon the bass dwindled, bg and bcp stunted. Now its a total mess in the process of getting back to a big bcp and bg pond.
I would say it is entirely possible to have BCP in a pond and keep them under "control" but it is a delicate balance and you'll have your hands full.
Pre and post BCP time of year I can easily pick off 100+ from 5-6" in an afternoon of fishing weed edges.
Was this a pond you did the initial stocking of? I'm optimistic I can improve the balance in my pond as it hasn't been actively managed for at least 5 years until my purchase of the property. Former owners ex-husband had bucket stocked it with crappie and perch. So far I've removed (and eaten) at least 80 crappie and one white perch (only one I've caught) - all bass and bluegill have been thrown back.