I like the idea, it makes sense that you'd become more desensitized over time. But I disagree with the proposed hemophobic/agoraphobic/claustrophobic changes, because those need to be situational and not just a generalized increased chance to panic.
In those situations, your level of panic would be calculated as if you have a lower courage skill than you actually do, but your base courage skill wouldn't actually change. If your courage is 10 you'd never panic, but if you're also hemophobic your chance to panic would be calculated as if you were an 8 or 9 but only in situations where you're bleeding. So a fully desensitized person would still have a chance to panic due to blood, but it becomes very low.
I also think the way to level it should just be kills. You kill 1000 zombies, you're probably gonna be desensitized. I mean thats kind of the underlying assumption of the "veteran" job and associated perk too, that this veteran has become desensitized through exposure to war and death.