If you "needed more meat", why didn't you shoot the doe?
She probably would have been better eating. "Cull" is just an excuse to shoot something. I wouldn't shoot a buck I wasn't going to mount.
You can't affect genetics by shooting deer in a free ranging herd, therefore "culling" is an impossible task.
If you were happy with the buck and shot him, wonderful. No need to bring culling into the conversation. It was public land and he was a legal buck. Asking other people what they would have done may not always get you the answers you're hoping for.