As somebody who has by now lived in 2 countries with Universal Healthcare I can answer that:

• It’s for people who want faster access to non-emergency medical treatment than the public system will provide.

So if you want to not to have to wait months for specialist appointments and surgery and you can afford it, you get Healthcare Insurance. This even more so for aesthetic and run of the mill dental treatment - the Public isn’t going to, for example, just put you in front of the queue to give you an implant unless it’s deemed necessary because of your health, so if your concern is about your appearance you’ll have to wait years or it won’t even be covered.

Mind you, the whole thing is still backed by the Public Healthcare System: if during a surgery at a private hospital you have massive complications they’ll generally transfer you to a Public Hospital.

Further, even in the Private everything is way cheaper because of the massive competition from the Public System, plus the Public even uses its leverage to keep the prices of more common medicine low (basically since most of the prescriptions are done by doctors in the Public System, for things were there are multiple options the most expensive stuff doesn’t get prescribed unless it offers enough benefit versus the cheaper options to justify it, so for example things like Insulin are way cheaper if you get it without a prescription from a Public System doctor and free or near free if you do because the State pays most or all of the price)

Anyways, the single biggest benefit of Universal Healthcare which the “free market is the best” (in this case it isn’t: in general the free market optimizes for profit, not for outcomes, and further, in this domain people will pay whatever it takes to survive and don’t actually have the expertise to judge the quality of treatment and know the availability of other options, so there is no natural free market here) crowd forgets is the peace of mind and freedom Universal Healthcare gives:

• if you lose your job, you’re still fine even if you have and accident or get sick
• if you want to change jobs you have total freedom as you won’t be without Healthcare for you and your family in the period between jobs
• if you need or want to stop working on a regular jobs (because you want to start your own company or want to take a sabatical or want to go back to school and get a degree) you can without losing your Healthcare coverage during that period and it’s going to be way cheaper than if you had to pay Health Insurance (and copays) during that time.

Private Healthcare Systems are very much prisons that keep people tied to traditional jobs,