An example of a country with "good healthcare" and such a system would be Germany. Extra insurance does exist there as well nowadays from what I understand but health insurance isn't tied entirely to employment and the extras are things like a 20 EUR per month to cover the co-pay on large and expensive procedures. While private insurance exists there too, I want to compare to the often touted "free healthcare" i.e. public system. There are still different providers even under the one public system.
So from a quick search, Germany has insurance rates from ~14-16% of gross salary, half of which the employee pays from their gross salary. But most insurances have an extra percentage they charge on top. I found one as an example that charges 17.29% total, which if you're self-employed, you have to cover yourself (to be comparable to your marketplace bronze plan being entirely self-paid).
Now the question becomes: Are you paying more or less as a percentage of your salary and by how much?
(and side question for your parent I guess: how does that compare to the $10k the employer pays, which would be 8.645% in this example)