I was thinking that the picker killed fewer mature birds than the combine. What about nest destruction? I don't have an opinion, just know that when combines came to southern PA, the pheasants disappeared.
I can't imagine a mature pheasant just sitting without flushing or running as either a corn picker or a combine ran over it. And while I have chopped up a few baby rabbits while brush-hogging, more mature animals or birds take off well before the tractor gets too near. But my Uncle did deftly swoop down and grab a ringneck pheasant by the neck as it sat tight on a cold rainy day when I was in my teens. A quick twist, and it was in his game pouch without firing a shot. According to my Dad, he also did that on several occasions with rabbits. He said the secret was to just keep walking without breaking stride when you saw one sitting, and quickly grab it without making eye contact. I never managed to do it before they flushed.
In Northern Pennsylvania, the native ringneck pheasant population crashed very quickly after the Game Commission decided to permit harvesting hens north of Interstate 80. Purely a stupid decision that they were too obstinate to admit was a serious mistake. Imagine trained wildlife biologists unable to figure out that killing off the mommy birds would drastically reduce the number of baby birds. That was a huge factor in my opinion, but clean farming techniques also reduced cover and the real nail in the coffin was the introduction of the Eastern coyote and protection of hawks. Native birds are all but extinct in most of the state now. A very small number of stocked birds survive to breed before predators get them. Attempts to replace ringnecks with Sichaun Pheasants, without correcting other factors, failed miserably too. We have also had a severe decline in ruffed grouse numbers, and nobody is using herbicides or combines in the grouse habitat. One expert here claims that predators actually increase game bird numbers. Here's a photo of a coyote attempting to protect a pheasant from freezing to death!