Any federal system will always be fiscally constrained by what folks are willing or unwilling to pay for it.
The military is bankrupting the country ... is it a failure because it costs more than Americans are willing to pay.
Importantly, is the military system and structure fundamentally flawed "broken from the start" because the citizens do not fund it at cost?
Finally, your argument requires that for any system to not be broken from the start that it accurately forecasts its success and the costs of the future ... things that simply do not exist.
One of the consequences of medicare is the old bastards keep living longer ... oooops, damn thing works too well. If we had public health for babies the next thing you know those bastards would start living too ... a catastrophic failure for sure. Thankfully we have private coverage for babies and can fortunately keep that system (the unbroken system) liquid and affording a rank of 31st in infant mortality rate, and 34th in child mortality rate. Maternal mortality rate .. same story. These are the folks served by the private system.
On these measures the US is essentially on par with former soviet republic eastern bloc countries.
I do not doubt that if we switch back to private insurance for senior age category we could get the fiscal house in order ... it would occur through reduced life expectancy.