The idea that armor increases injury risk is a fascinating case study of unintended consequences.
Similar “safety irony” claims I’ve heard include:
* Mandatory bike helmet laws increase total risk to life because having to wear a helmet deters people from cycling so they drive instead, and thus miss out on the increased cardio health they would have got from cycling.
* Trains are too safe, meaning they have to meet such stringent safety criteria that the costs are raised to the point that people drive instead, and driving is much more dangerous.
And my favorite personal anecdote: a ruined castle in Portugal which had a staircase leading up to a high ledge with no barrier. It was so obviously dangerous that everyone was taking a lot of care up there…