What type of trap are you using... Some traps like fyke nets are pretty darn efficient and will certainly catch a lot of BG. Something like a simple cylindrical minnow trap will not make much of a dent...

Now if you did catch a ton of BG in a fyke net which is very possible... The amount of work it would take you sort through the fish and cull out the ones thought to be inferior would be very time consuming. If you were willing to put in the time and purchasing a fyke net of substantial size, I think you could make a dent in the BG and you could cull out fish you felt were not desirable. The biggest trick would be deciding which fish were inferior, slow growing etc, while figuring out which were superior, fast growing, etc...