You don't get "extremely good" (as the GP wrote) service at a 3 star hotel. Less than 1% of the population uses 5 star hotels. In Finland over 50% of the population use private health care (either directly or via their work contract).
Edit: As a commenter pointed out it's 50% that use private health care, too. Very few people would exclusively use private health care.
If you can afford it (or your employer pays for it), you get to use whatever. It helps cut some queue times, and gives you more choice and convenience.
Doesn't mean the free one can't still be "extremely good". I might pay for IntelliJ, even though a free IDE or even editor like Emacs is still extremely good.
And 40% of the population is still a huge number of people, who would otherwise had trouble affording private health care or get the shitty low tier and/or hella expensive private care afforded by the poorer in the US.
It's also not exactly like "50% of the population use private health care". It's more like "50% of the population ALSO use private health care", in addition to the provided free health care.
Well, in the end the employer has reduced your salary by that amount, employers are not known for welfare. Every employee is already entitled for full public health care. Something must be wrong with it if 90% of the employers offer double insurance in away. It's a public secret or gentlemen's agreement that employed people are not supposed to use the public health sector they are entitled to before they need specialist or hospital treatment. The gentlemen's agreement would stop working if basic public healthcare were reasonably good.
Edit: As a commenter pointed out it's 50% that use private health care, too. Very few people would exclusively use private health care.