In Israel and Switzerland do have private insures funding everyrhing as far as I know but I migth be wrong guys.
Something that's interesting is that these two countries (plus a few more) often come up in free-market / libertarian type arguments as some kind of examples, however a bit of fact-checking usually reveals some flaw in the argument, or some specific circumstance of that nation that just can't be replicated elsewhere. They're usually very small nations, often act as tax havens, or trading hubs. Hong Kong and Singapore are the two other nations I seem mentioned in this context.
For example Israel and Switzerland are in a relevant list here:
https://en.wikipedia.org/wiki/Health_care_systems_by_country#Countries_with_universal_private_health_insurance_systemUnder "Countries with universal private health insurance system". The total list is Liechtenstein (a well known tax haven), Switzerland (an even better known tax haven), Netherlands (a small nation but with an extensive global financial empire) and Israel (a very small nation, and
also a noted tax haven). So in other words many of these small but surprisingly wealthy nations which can afford to have these privatized-but-subsidized health systems turn out to have vast financial empires which exploit the larger nations around them with ways to dodge paying taxes.
Also note that for a very small nation, running their entire health system themselves would not leverage the "economy of scale" thing, so in that case, it would have nothing to do with public vs private, but it's just cheaper to allow a nearby foreign company to provide the service. For example if Lichtenstein allows French companies to provide health insurance then all the infrastructure for that is already established in France, so it saves Lichtenstein from having to replicate it: all the software and apps to run the thing would be French and already exist. So, for a tiny nation like Lichtenstein "private health insurance" totally makes sense, but only because implementing an entire local system would be too expensive for such a small nation, and, secondly, because the
national health system in France can't legally operate in Lichtenstein, so it has to be a private company because those can operate over borders.