To touch on a few points that I saw in this thread:
Travelex and Berkshire Hathaway are Primary payer, and will place a Guarantee of payment on your behalf (If they can get an invoice form the clinic) if you are disembarked, and admitted to a hospital/clinic.
Ships do not accept insurance.... Period.... you have to pay on your ships card
Travel Insured Intl (USAA, WTP) policies may be Primary but are pay and cliam
Travelex will prepay for all insured to fly back home upfront, TII and AON do not only the Patient and a medical or non medical escort (if needed)
Medical coverage offered by the cruises lines is low, so is the EVAC for anything other than the Caribbean.
I cannot speak to how Allizanz works.
If you have insurance, other then the cruise insurance and you see the ship Doctor or have an accident on shore, let the cruise line know so they can contact them.
My Recommendations for the Caribbean:
If you can pay of a day or ten of medical upfront the cruise line insurance I don't think looks at your age just cost and length, so maybe cheaper.
They usually offer 25k (NCL, Princess standard, HAL, RCCL, Disney, Virgin Voyages) or 30k (Carnival) or 50k (Princess platinum) for emergency evac.
The Evac benefit will get you to the closest hospital if you cannot get home medically safe. Then once are you the costs to get home come from the same benefit, including if needed a nurse.
Most port hospitals are familiar with the various travel insurances. They know which ones will pay and which will not (usually)
Cruise line insurance is secondary only and will only place a payment to prevent you from being held, or to secure admission. 10-25k they offer doesn't go far just like in the US for most of these hospitals
Outside of the Caribbean:
50k + of medical as primary, and will pay if you are inpatient (Travelex, BHTP) without question.
100,000 -250,000 For evacuation benefits. An Air Ambulance from France to say I duno Kansas will be 75,000 to 150,00 roughly depending on the level of care you need.
Viking Cruises is the only line I know of that uses a different company for their insurance, they are also secondary and excess.
**The opinions here are my own and do not reflect that of my employer*** I do not sell insurance, I do not support one company over another, they all off their own services that may or may not work for you.