First line in Wikipedia (https://en.wikipedia.org/wiki/Healthcare_in_Switzerland) There are no free state-provided health services, but private health insurance is compulsory for all persons residing in Switzerland (within three months of taking up residence or being born in the country).
The difference being their version of the individual mandate was not struck down or watered down to becoming a 'penalty'. Instead it was like what we do with auto insurance.
Most "free" healthcare systems have either (1) horrible quality of service or (2) impossibly long waits unless your life is in danger or close to it. The latter is a systemic issue I've noticed in that healthcare, regardless of pricing or structure, does not aim to foster optimal health, but merely to prevent mortality - so if you go with a 'minor' issue such as recurring headaches or chronic fatigue, it will be dismissed entirely.
I don't have the right answer here and am all for people having affordable options from 'free, wait 3 months' to '20K, full service now', but once again, personally speaking, I'm not rich enough for 'free' things. I'd rather pay and know exactly what (and in this case, much more importantly, when) I'm getting. And from what I've noticed, my personal beliefs that people should strive for optimal health rather than mere preservation of life, is a popular opinion deemed 'unrealistic' by experts.
So I'm not sure what constitutes "most free healthcare systems" but Canada is apparently different from "most"
We generally call this the 'Iron Triangle' in healthcare policy/management. You basically get a pick at most two out of (1) access, (2) quality, (3) cost.
As to your general sentiment healthcare is a bit 'one size fits all' when in terms of insurance/reimbursement solutions. Note that the needs of the aforementioned triangle are weighted differently based on acuity of care. More generalized simple/low acuity care we are happy to get low cost and ready access as our best solutions (e.g. minute clinics, online/virtual care/telemedicine for getting a vaccine or pinkeye/localized infection without complication).
Meanwhile ER representing the other spectrum we instead have greater need for higher quality and access. You must get to an ER ASAP and get stabilized.
Chronic care quality solutions with long term cost-effectiveness are what are needed. Access to a specialist for longer term condition management (or episode or care like a cancer diagnosis).
Similarly more procedures are becoming outpatient, or recovery at home, or at dialysis centers, or at skilled nursing facilities ... you get the point.
I argue the problem is that the insurers have not adequately fragmented the insurance market/reimbursement model. Healthcare is changing in how it is delivered and insurers are not keeping up with it when it comes to modeling their payouts. For example why does being in-network matter for low cost care at outpatient facilities? The added 'negotiation' of being in a specific network doesn't add much value. One size fits all doesn't work with the modern spectrum of care.