The use of the organic label is to distance people from this imagery by constantly repeating the propaganda that everything is being done 'nicely'. However, actually showing any kind of killing, no matter how nice, destroys that propaganda. The key trick is to use the correct words to make sure people do not conflate what they are eating with anything negative, and the organic label is part of that.
When you go deeper and attempt to explain how the killing is better, you simply open the audience to the fact that there is still killing being done. This is the wrong approach for the target market. It's better to distance the brand from the actual realities as much as possible.
We fear our own deaths because we've forgotten our true nature, so we've attempted to banish the specter of death from society as a whole. I'm willing to bet people who have this reaction to the death of a chicken are being brought in contact with their own mortality, and that scares them. Given that we are all going to die, we should get comfortable with death rather than hide from it.
Hint: they don't run around in happy green fields.
Some of them do. I actually check the code on eggs before buying to make sure I'm getting those from free-roaming chickens.
Not to mention that farmed chickens are bred to be so fat they can barely walk anyway: https://www.wired.com/2008/02/chickens-cant-w/
Me, I figure there's all sorts of tasty critters in the world and I'm willing to try every one.
Most people cannot really identify with thousands of chickens in a cage being processed by a machine - but they can identify with a single chicken happily running around outside being taken and killed. So paradoxically, the second image would actually be something they see as even more cruel.
Informing people about this has to be done in a very clever way to ensure that people don't connect the packaged breast they buy with the actual chicken running around outside. One slip up, and your label becomes worse than the factory chickens.
While the people who choose to come for a farm tour likely know what to expect, the 'average' consumer would not react in the same way to being told that they're eating this happy, free ranging chicken. As with all marketing, it's important to come from a position of your customer's lifestyle than your own where you 'know' about death.
To put it in a completely different context - think about Target and their new bathroom policy. On the surface it seems great, and everyone supports it. The label is wonderful and everyone wants to be part of that movement. But when it actually comes time to go to a bathroom, many women freak out and refuse to actually enter that bathroom anymore. It's even costing Target customers, and now pulling back the policy would cost them even more. Marketing isn't easy and you need to fully understand what you're doing before you end up creating a marketing campaign that actually harms your business.
Once you understand that, you understand why the label is the single most important thing, and the less real details supplied the better. Any details you supply serves to break the facade that the organic label means you're doing good deeds - because ultimately, you're still killing that chicken. It's why "efforts to broaden beyond just an organic label" are doomed before they begin and will hurt sales more than they help.