This is not the case. You have to make sure you have insurance or the government will fine you. But if you were unable to get insurance for whatever reason, you still don't have insurance.
And Obamacare premiums are not small and the insurance is not very good.
The worst conforming ACA plans are essentially the catastrophic insurance that people think they are clamoring for; they are expensive because health care costs in the US are spiraling out of control. It could be that people actually want plans with a bunch of complicated limitations and limits, but I doubt it.
Just an anecdote, but I have not found this to be the case at all, and I'd figure I'd offer an example of one such "clamorer who thinks he wants catastrophic plans" to balance the discussion.
Prior to ACA I was on a "catastrophic" plan (despite being able to afford something much more comprehensive). I think the "catastrophic" term is kind of dumb, and I'd instead call it "actually-insurance, not a prepaid health subscription".
The premium was around $95/month and I spent maybe another ~$1k/year on medications and office visits. I was totally satisfied with this health coverage and never felt I had to limit my access to health care because of my plan.
As soon as ACA rolled around I tried to find the most similar plan I could (mine was discontinued despite promises to the contrary).
1) I couldn't get as high a deductible, so I was forced to pay for risk-reduction I didn't want. In an absolutely life-threatening 1%-of-insurees catastrophe, my family can absorb say $25k/year out of pocket so I see no reason to insure against that financial risk.
2) The first year my premium was $180, then $220, then $260. I did not save any money on medications or office visits (if anything it got more expensive, but that may also just be a general trend in US health costs).
So post-ACA my insurance premium cost has nearly tripled, and the product I considered satisfactory before is simply not available on the market.
In summary: people can rationally prefer pre-ACA catastrophic plans, and post-ACA such options are not available.
Government can merely redistribute its tax earnings, often in extremely corrupt and wasteful ways. It does not create wealth on its own.