Proof of this here: https://www.backyardchickens.com/threads/another-reason-to-build-a-full-height-coop-run.1484191/
Also, height is your best friend when it comes to ventilation since it enables you to put the vents well up above the roosts -- allowing a free flow of air without risk of feather-ruffling drafts on the roost.
Yup thinking of your injury every time I read a height that can lead to things like that.