Earlier quoted context omitted.
You are not getting health insurance in most European countries unless you are working or registered as unemployed and remain at disposal of the local job centre. And the whole meme that a 65% tax rate +25% vat on most products on top of it (I am in Sweden) is somehow worth it financially because "fReE HeAlThCaRe" is laughable.
To be clear, I'm merely saying "the complexities of the American healthcare system might be why Europeans are more inclined to take gap years". That said, I didn't know that European public health insurance was commonly contingent on employment. I would be curious to know more about this.
The easiest way to afford it is to have a job. However, if you are willing to pay more (still much less than equivalent US health insurance, e.g. in Germany around 180€/mo) you can buy it directly. Or, you can participate in that country's social safety net which, yes, usually requires you to actively seek a job (often for some loose definition of "actively.")