A high-deductible health plan can still leave you writing a large cheque before coverage takes over. Accident insurance is built for that gap: when a covered injury happens, the plan pays a fixed cash benefit straight to you rather than to a provider.
Because the money comes to you, you decide what it is for — the deductible, the mortgage, the weeks you cannot work. Benefits are scheduled by event, so you know in advance what a fracture, an ambulance ride or an emergency room visit pays.
This is an add-on and never a substitute. Accident cover alongside a comprehensive health plan is sensible; accident cover instead of one leaves you exposed to exactly the costs that bankrupt people.