(edit) - and just to reflect on what happened to this child, in addition to the physical changes & social problems, this "treatment" would have surely induced gender dysphoria, which any trans person can tell you is awful as hell.
That's orthogonal to universal healthcare or even a single payer system. There's nothing preventing you from having the whole country be represented collectively, but still have private insurers, like in germany. https://www.commonwealthfund.org/blog/2019/how-drug-prices-a...
Not sure if this is an earnest defense of the state of healthcare costs in the US but you'd have to be deluded if you think that the rampant profit-seeking in the US for healthcare is merely the cost of doing business.
It's brand name drugs that are cheaper in other countries.
[1]https://www.who.int/intellectualproperty/events/en/R&Dpaper2...