Health Insurance Reform-Beware of the general solution for the specific problem

I am concerned about the direction of the current debate on the reform of our health care system. Most proposals for reform are based on two premises.
The first, is that our health care system is overrated and not equal to some that use a different model for health care , like the single payer systems of the United Kingdom and other European countries.
The second is that 47 million Americans are "uninsured".

Neither , in my view, is correct. Both come from the unfortunate tendency to tear something down when proposing something new. Afterall ,who will take a proposal to fix something seriously unless the something is totally broken.
It is the second premise I want to address here because the phrases "47 million Americans are uninsured", or " without insurance whatsoever" are used as if this was one homogeneous group to show that the american health care system is broken.

So , let's look at the makeup of the 47 million figure dervied from the US Census Bureau figures.
1. 27 % , or roughly 12.7 million people, are uninsured for only a part of the year in which they are counted but are ultimately insured. This is an issue or portability of health insurance. This group will need plan A to reduce their risk of becoming ill while not covered by insurance . But are they really " uninsured" in the way the term is usually used?
2. Roughly 10.3 million of the 47 million are listed as " not American citizens". They require Plan B which surely has more to do with immigration reform than reform of the health care system. Most proposals use the 47 million uninsujred total but ignore the fact that a substantial part of this group are illegal aliens.
3. The third group is made up of roughly 9 million people, half of which make between 50 and 75 thousand dollars a year and the other half more than 75 thousand dollars a year. Many of them are healthy young people who can afford insurance but do not wish, for various reasons, to buy it. This group, if they must be covered, would require a plan that required everyone to buy health insurance, say, Plan C.
4. In the 4th group, there are roughly 8 milion people of all ages, adults and children alike, who are actually eligible for health insurance under a variety of existing plans but don't take advantage of them , again, for a variety of reasons, sometimes out of ignorance. Surely we can solve the problems of educating people about the existence of these plans using Plan D.

That leaves the 5th group, roughly about 7 million people, who might be called the " hard core uninsured" or "without insurance whatsoever", certainly a tragedy for a country as rich as ours . This group will require Plan E.
But the 47 million uninsured figure is quoted as if all of them are hard core uninsured which is factually incorrect .
It is important , it seems to me, to examine the issues related to these groups separately, and to hear specifics about plans A through E so we do not apply " the general solution for the specific problem" and do more harm than good to the finest health care system in the world..