1. The reason why healthcare insurance policies are counterintuitive to other insurances is to foster preventive care. If I am covered only for catastrophe, then I will sit and wait for the catastrophe to happen rather than going and getting things fixed early. Because, from my perspectives, my costs are identical in both cases.
2. What constitutes a catastrophe varies wildly with person to person. For someone earning 1,000,000 per year, it could be that a bill of 500,000 is a catastrophe. But for someone who is earning only 10,000 per year, a bill of 5,000 is a catastrophe. The cost of covering a person earning 10,000 per year would be orders of magnitude higher (which he wouldn't be able to afford) than the cost of covering a person earning 1,000,000. For this reason, the insurance HAS to be provided by some agency like a government which can take losses on covering someone who is earning 10,000 and recover some of the insurance costs by charging a premium to the person earning 1,000,000.
3. The model could be as follows. Currently, govt collects 7.5% as Medicare. This 7.5% can be increased to say 10%. But now Medicare will also come cover the person paying the premium in the following manner: The person is covered 100% above a certain threshold which is the function of his/her yearly income (So for example, a person earning $10,000 is covered for all medical expenses higher than $1,000. Someone earning $1,000,000 will have their coverage begin after they spend $500,000). In addition, all are allowed to purchase secondary insurance from the various insurance companies if they so desire (to limit their loss during catastrophe).