The core purpose of Accident Insurance is to help pay for certain, specified expenses arising from accidents.  All carriers offer a base policy with a schedule of compensable events and a corresponding benefit.  A typical policy will list 50-70 different events.  For example, knee surgery with repair may pay $500, hospital Admission may pay $1,000, an urgent care visit may pay $75, and so on.  

A secondary purpose may be income protection against accident risk, to the extent a Disability Income option is available.

The concept has been popularized by the famous duck in Aflac commercials, but most such programs are geared toward the employer-sponsored workplace market.  This page identifies alternatives to Aflac available to individuals on a standalone basis, without employer involvement.

A base policy alone would not protect income, but a Disability Income rider would.  For our purposes, the whole point of Accident coverage is to acquire a Disability Income rider, which narrows the universe of contenders.  Carriers that don't offer a Disability Income rider are ruled out.

The advantage of an Accident policy with a Disability Income rider - compared to a Disability Income policy that is limited to accidents only - is more relaxed underwriting and therefore greater accessibility.