Both. Please notice I prefaced the remark with "Generally".
Both balance and mobility are reduced as we age. Injuries from falls can cause bone fractures and head injuries. These types of injuries are harder to recover from as we age. This I know from personal experience.
As for scientifically proven, the CDC has stated that unintended falls are the leading cause of injury and accidental death in people over 65.
This report describes the percentage of nonfatal and fatal falls among older adults during the previous year.
www.cdc.gov
Step ladders amplify the danger because you're falling from an increased height, increasing the injury's severity.
I grew up in farm country. It was an everyday occurrence to see men over 70 on ladders, working on roofs, and climbing into tall machinery. I know many here do as well. I know many of us over 70 (yes. I'm a member of that club) are still active and working. However, the risks of stepladders and the long-term injuries to people over 70 are significant and should be recognized.