<font color="#FFFF00">"...and let the big one stay in the gene poll
This seems like a valid concern.
It's also a theory often spouted by anti-hunters in protest of trophy hunting. They like to exploit what they perceive as controversial issues to create discord amongst hunters. Divide and conquer if you will.
An important fact has to be ignored to buy into this flawed theory: It took several years for that buck to reach its trophy size. He has been donating his genes to every doe within miles for all those years. Meanwhile, his offspring have been doing the same. You are not removing that animal's genes from the pool. They will always be there.
Also consider that if taking trophy animals from the herd was in fact detrimental, then why do the record books continue to grow from year to year? The opposite would be the case if that theory were true.
I'm not advocating one position over another. Just do what you think is right, and don't be swayed by propaganda. Think for yourself.