If it gets to the point where I'm quitting because of it, why would I bother giving them the record of evidence? Why would I want to improve the organization that I am leaving?

Put explicitly, if the work culture is such that I don't have reasonable avenues to improve the situation without quitting (e.g. via HR and skip level), then I really don't care to help them out when I've given up hope for them. If they want to improve, they should set it up such that the only way to improve is by employees quitting. People usually don't quit capriciously. It's a tough decision, and a lot of work to find a desirable alternative job. I don't want to give them charity on my way out, especially if they've wasted a significant amount of my off-work time looking for a job.