It's good to provide humane care for the animals. It's simply a good practice of being a higher-order animal like us.
Nature is cruel, but we don't have to carry on the cruelty of nature out of the flawed logic that because nature is cruel, we should practice the art of cruelty. We know better, and can achieve better. So why not?
Now, the OP confuses me, because none of this has to do with the free range and organic movement, at least, not entirely. That movement does provide for more humane living conditions, in that they get to roam where they want to instead of being corralled and fed empty nutrients to fatten them up. That said, the movement is more about the actual quality of the end product for consumption, in that when they eat their natural free-range diet, we get meat with a better nutritional profile.
Knowing the process that goes into butchering simply sucks, there's no way around that. It is a part of our nature in that we need to consume these animals, and the best butcher practices are long-removed from the natural stylings of strong-jawed carnivore kills.
For those that feel sinful knowing that an animal had to be quite grotesquely killed in order to fill the plate at the table, I can't really offer much that would soothe the soul. It sucks, but there's not much else that can be done.
To do it the most humane way possible, and to provide quality living conditions, is the best we can really hope to achieve. But do note that quality living conditions does not require getting the most natural diet for the animal. For their short lifespan, bad diets full of harvested grains is not going to negatively effect their lifestyle and health.
Which is to say, we can have humane conditions and best-practice butchering and yet still have less-than-ideal nutritional profiles in the resulting meat. So we should opt for the best of it all: natural grazing diets with quality living conditions and "humane butchering", so that our soul can rest easy and we can get the nutrition we should be after in the first place. Sometimes that comes at the cost of taste in the eyes of some, as many prefer excessive fat from grain feed, whereas grass-fed/free-range meat is typically far more lean. I am of the opinion that the best nutrition should be our optimal goal, or else why are we eating a particular thing? And that happens to coincide perfectly with the ideal living conditions for most animals we raise to consume.