Since Obamacare is "not the best way" of providing universal healthcare, how would the US go about providing such a scheme for all of it's citizens? Assuming Obamacare is scrapped, to start off with.
Step 1 - Go back to the pre-Obama care healthcare system. Under that scheme about 85% of the population was covered with insurance. Most were reasonably happy with it and don't want the government screwing it up.
1. The poor were covered by Medicaid (about 20% of the population).
2. The elderly are covered by Medicare. The middle and upper class elderly supplement this by private Medigap policies.
3. The majority of the middle class (about 55% of the population) is covered by group private insurance provided by their employers or unions.
4. About 5% of the population purchased private insurance.
Step 2 Deal with the 15 % uninsured and only the 15% uninsured. It's a lot easier (and cheaper!) only to deal with this group than to try to do the universal thing Obamacare is attempting.
People who are not covered by the above include self employed, people who retired early (Medicare starts at 65), people who work in lower middle class jobs (the not quite poor who make too much to qualify for medicaid) etc. The biggest losers under the old system were individuals with chronic health conditions (complicated diabetes, autoimmune disorders, etc) who were uninsurable.
1. Have a government high risk pool for the uninsurable. Model it after Oregon's which namelessfly says works well. Individual states could design their own variations to fit their needs.
2. The one popular part of Obamacare was that the young uninsured are now eligible to stay on their parents' policies until age 26. Reinstate that part as a stand alone law.
3. For the not quite poor (income limits apply), the self employed (proof of self employment required), and early retirees (59 1/2 and above, the same age at which you may start accessing 401Ks).
Part 1 - Make available government subsidized catastrophic insurance to those in these 3 groups. The catastrophic issues are what the people in these categories really worry about. Those are what can cause bankruptcy and destroy lives.
1. Major accidents such as car accidents but not minor accidents such as a broken arm.
2. Treatment of major diseases such as cancer but not cover minor diseases
3. Maternity coverage for women of childbearing age
4. Not cover most medicines, only cover very expensive ones such as those used to treat cancer
5. Not cover most physical therapy, only cover extensive physical therapy such as that following knee surgery
6. Not cover mental illness
7. Not cover preventative care
8. Not cover vision or dental
9. Not cover addiction treatment
Part 2 - Have private insurers provide catastrophic gap policies for those in this group. Similar to Medigap policies, covering the things that the government provided catastrophic insurance doesn't. Individuals could choose to buy the gap policy or not as they so chose.